For those who budget other aspects of their lives, this is pretty straight forward. For those who don't budget anything, this may be like a foreign language. Regardless, I shall tread into these dangerous waters.
Some aspects are easy and others far more difficult. Step one is just to make sure one is considering all aspects of ownership and not overlooking an item that could shock them. I budget for one simple reason, I don't like surprises.
Purchase Price
The biggest thing here is to add in all the costs anticipated in the first year to get the boat to where you want it. More than any other boating costs, these tend to be drastically underestimated. Don't assume more DIY than possible. Look at yard rates too.
Depreciation, Interest, Mortgage
Mortgage and interest on a financed boat are easy to calculate. One pitfall is many are sold on financing based on the interest being tax deductible. Careful, as it is deductible but only by itemizing and benefits you only by the amount it increases your deduction. Fewer and fewer people each year are able to benefit.
Transport
This is typically a one time expenditure at purchase for getting the boat home. However, some boaters do want to shift cruising grounds later and that incurs a cost.
Dockage
There are two components here. First is your home dock. Second, is docking while cruising. In both cases don't overlook electric, water, cable, trash, pump out and any other costs. Also consider size of boat. Not only does a bigger boat give more linear feet but often the price per foot increases as the size does. If you intend to anchor while cruising, don't overlook places you might use mooring and the occasional marina.
Fuel
Base it on anticipated and desired usage. Don't assume you will always run at the most economical speed, use a balance. And, don't assume today's fuel prices will stay. Here like everywhere else in budgeting you need to allow for inflation. Also, don't overlook fuel for your generator or for your dinghy.
Routine Engine Maintenance
This may vary widely based on location, brand of engine, number of engines and what work you will DIY vs. using yards. Start with the owners manual and recommended maintenance schedule. Talk to some mechanics or yards about prices. Don't overlook the prices of filters, impellers, and fluids. Engines should include your generator.
Contingency Engine Maintenance
Things will break. Talk to other owners about major expenditures they've had. While you may not need a rebuild, you will at some point have some unexpected service requirements. As to a rebuild, at least know worse case and have a contingency plan if it ever comes to that.
Other Equipment Maintenance
Every piece of equipment will at some point require maintenance. Repair of shafts and propellers can be very expensive. Don't overlook electronics repairs, stabilizers, thrusters, toilets, holding tanks and pumps, watermakers, refrigerators, laundry equipment, oven, dishwasher. If it can break, it will. Your best source is crowd sourcing owners of similar boats, but be specific in what you're asking so it's comprehensive.
Electronics
Consider the likelihood of upgrades and the costs as well as the costs of updating charts and software. Electronics have shorter lives in general than most other boat equipment. Much has built in planned obsolescence.
Deck, interior, hull and superstructure routine maintenanceThis would be cleaning, diving, including supplies if you do it yourself. If teak or other wood, the maintenance of it. Include bottom painting at whatever frequency is required. Do not underestimate the cost of any haul outs.
Major on deck, interior, hull and superstructure
Know the costs of replacing the teak deck or painting the entire boat, the cost of redecorating the interior if there's the possibility of that need arising.
Dinghy and toys
These items have initial costs but then often have limited lives. If the outboard is old, what is the cost to replace? Will you be satisfied with what comes with the boat or want something new? What about kayaks, bicycles?
Communications and equipment
Satellite tv? Internet? Subscriptions and equipment. Cellular phones with additional phones for different areas? Cost of data. New televisions, tablets, computers.
Insurance
Find out what others are paying but also what it includes. What will be your cruising ground? Will there be surcharges?
Taxes and Licenses
This starts with purchase and sales tax, but I consider that a cost of the boat. Property taxes vary significantly on location. Consider your present location but also future plans. Add in registration and documentation, then include cruising fees and customs fees for places you might go. This would include canal permits too from the NY Canal system to the Panama Canal. Many are shocked at the charge in the Bahamas, so don't overlook it.
Shipping, postal, etc.
If you're cruising, there will be a cost for handling your mail.
Travel and lodging
These are the costs of traveling to and from your boat if any. Some leave their boat away from home periodically. Also, costs of lodging while boat is on the hard.
Ordinary Costs of Living
There is a tendency to say that this will be the same as if on land. Only if you maintain the exact same lifestyle. Some find it much less expensive as they eat for less and don't incur auto expenses as much. However, if you check out all the fine restaurants in San Francisco or New York, go to the opera or a Broadway musical, it will be more. Don't overlook entertainment costs. It's a shame if you go to great places but don't enjoy them because you didn't anticipate the cost. Also, anticipate guests and any arrangements there. Perhaps it will be less than when you're home on land, or perhaps more.
Recommendation
My recommendation is to take one's best shot at all these things and then add some level of contingency, 10-20% perhaps. Budgets are just projections, but by having one at least you'll know where your initial estimates are high or low. The biggest purpose of all this is to be able to enjoy whatever boat you buy without feeling financially stressed. If one boat is stretching your tolerance and resources, then enjoy a boat that will not.
The best time to get a feel for costs is prior to purchase. To me, boating pleasure is greatly enhanced by knowing, even the surprises, I planned for. I build reserves for major items, either on paper, or actually in a bank account.
I'm sure I've overlooked some items others consider important and I hope they'll be added. Also, I hope some will note the areas that have cost them far more or far less than they anticipated.
Some aspects are easy and others far more difficult. Step one is just to make sure one is considering all aspects of ownership and not overlooking an item that could shock them. I budget for one simple reason, I don't like surprises.
Purchase Price
The biggest thing here is to add in all the costs anticipated in the first year to get the boat to where you want it. More than any other boating costs, these tend to be drastically underestimated. Don't assume more DIY than possible. Look at yard rates too.
Depreciation, Interest, Mortgage
Mortgage and interest on a financed boat are easy to calculate. One pitfall is many are sold on financing based on the interest being tax deductible. Careful, as it is deductible but only by itemizing and benefits you only by the amount it increases your deduction. Fewer and fewer people each year are able to benefit.
Transport
This is typically a one time expenditure at purchase for getting the boat home. However, some boaters do want to shift cruising grounds later and that incurs a cost.
Dockage
There are two components here. First is your home dock. Second, is docking while cruising. In both cases don't overlook electric, water, cable, trash, pump out and any other costs. Also consider size of boat. Not only does a bigger boat give more linear feet but often the price per foot increases as the size does. If you intend to anchor while cruising, don't overlook places you might use mooring and the occasional marina.
Fuel
Base it on anticipated and desired usage. Don't assume you will always run at the most economical speed, use a balance. And, don't assume today's fuel prices will stay. Here like everywhere else in budgeting you need to allow for inflation. Also, don't overlook fuel for your generator or for your dinghy.
Routine Engine Maintenance
This may vary widely based on location, brand of engine, number of engines and what work you will DIY vs. using yards. Start with the owners manual and recommended maintenance schedule. Talk to some mechanics or yards about prices. Don't overlook the prices of filters, impellers, and fluids. Engines should include your generator.
Contingency Engine Maintenance
Things will break. Talk to other owners about major expenditures they've had. While you may not need a rebuild, you will at some point have some unexpected service requirements. As to a rebuild, at least know worse case and have a contingency plan if it ever comes to that.
Other Equipment Maintenance
Every piece of equipment will at some point require maintenance. Repair of shafts and propellers can be very expensive. Don't overlook electronics repairs, stabilizers, thrusters, toilets, holding tanks and pumps, watermakers, refrigerators, laundry equipment, oven, dishwasher. If it can break, it will. Your best source is crowd sourcing owners of similar boats, but be specific in what you're asking so it's comprehensive.
Electronics
Consider the likelihood of upgrades and the costs as well as the costs of updating charts and software. Electronics have shorter lives in general than most other boat equipment. Much has built in planned obsolescence.
Deck, interior, hull and superstructure routine maintenanceThis would be cleaning, diving, including supplies if you do it yourself. If teak or other wood, the maintenance of it. Include bottom painting at whatever frequency is required. Do not underestimate the cost of any haul outs.
Major on deck, interior, hull and superstructure
Know the costs of replacing the teak deck or painting the entire boat, the cost of redecorating the interior if there's the possibility of that need arising.
Dinghy and toys
These items have initial costs but then often have limited lives. If the outboard is old, what is the cost to replace? Will you be satisfied with what comes with the boat or want something new? What about kayaks, bicycles?
Communications and equipment
Satellite tv? Internet? Subscriptions and equipment. Cellular phones with additional phones for different areas? Cost of data. New televisions, tablets, computers.
Insurance
Find out what others are paying but also what it includes. What will be your cruising ground? Will there be surcharges?
Taxes and Licenses
This starts with purchase and sales tax, but I consider that a cost of the boat. Property taxes vary significantly on location. Consider your present location but also future plans. Add in registration and documentation, then include cruising fees and customs fees for places you might go. This would include canal permits too from the NY Canal system to the Panama Canal. Many are shocked at the charge in the Bahamas, so don't overlook it.
Shipping, postal, etc.
If you're cruising, there will be a cost for handling your mail.
Travel and lodging
These are the costs of traveling to and from your boat if any. Some leave their boat away from home periodically. Also, costs of lodging while boat is on the hard.
Ordinary Costs of Living
There is a tendency to say that this will be the same as if on land. Only if you maintain the exact same lifestyle. Some find it much less expensive as they eat for less and don't incur auto expenses as much. However, if you check out all the fine restaurants in San Francisco or New York, go to the opera or a Broadway musical, it will be more. Don't overlook entertainment costs. It's a shame if you go to great places but don't enjoy them because you didn't anticipate the cost. Also, anticipate guests and any arrangements there. Perhaps it will be less than when you're home on land, or perhaps more.
Recommendation
My recommendation is to take one's best shot at all these things and then add some level of contingency, 10-20% perhaps. Budgets are just projections, but by having one at least you'll know where your initial estimates are high or low. The biggest purpose of all this is to be able to enjoy whatever boat you buy without feeling financially stressed. If one boat is stretching your tolerance and resources, then enjoy a boat that will not.
The best time to get a feel for costs is prior to purchase. To me, boating pleasure is greatly enhanced by knowing, even the surprises, I planned for. I build reserves for major items, either on paper, or actually in a bank account.
I'm sure I've overlooked some items others consider important and I hope they'll be added. Also, I hope some will note the areas that have cost them far more or far less than they anticipated.
If I had numbers like that in front of me before I thought about doing what I'm doing. . .I wouldn't have done what I have done 
