New2... Situations can be intimidating but... you can maybe take a deep breath and then start breaking this down into smaller issues so you better understand what the problem is... and so folks can better help you work out what solutions might be.
1) Locate the holding tank
2) Locate and trace each hose connected to the holding tank
- one probably goes to the toilet
- one probably goes to the pump-out fitting on deck
- one probably goes to the vent fitting, perhaps on the side of the boat near the pump-out fitting
- one may go to an overboard discharge macerator (essentially a grinder, not unlike a household garbage disposor, conceptually), and from there to a discharge thru-hull
3) locate and trace each hose connected to the toilet
- one probably goes to the holding tank
- one may go to a direct overboard discharge,
- if you've got those two, you perhaps have a Y-valve to select routing to the holding tank -- the hose going to the holding tank mentioned above -- or directly overboard instead
- one may come from an inlet thru-hull (assuming yours is maybe a raw water (aka sea water)-flush toilet
4) puzzle out how those innies and outies work, i.e., what comes from where, what goes to where
Once you've got all that, you can maybe sort out what to do next. One idea, for example (and while we await further info) is that you could perhaps disconnect the vent line from the holding tank, and maybe use compressed air to blow that clear. Might be other ways, too, so that's just an example... but cleaning the vent line could be as simple as that.
Wouldn't hurt do try further to identify the toilet brand, and ideally model, too. Sometimes there's a label, sometimes you can ID with a Google picture search. Or post some pics here, and maybe somebody can identify. (Usually Peggie can tell them all.) If you can come close, you can often find the manual on line somewhere.
Might be a label on the holding tank, too, and that might include capacity. Might not be completely accurate, but might be a start toward deciding how often you need to pump out.