Long story short: where am i allowed to go?

I was at yellowstone this last summer and i was looking into getting a backcountry pass. in the process of inquiring i realized i have absolutely no retarded fucking clue about where i'm actually allowed to be and where i'm not. say i'm in yellowstone (just as an example), what's to stop me from just parking on the side of the road and walking perpendicularly outwards into the wilderness? am i allowed to to that? based on all the roads and trails, i'm left with the impression that every area is de-facto off limits with the exception of marked trails and such. this conflicts with the nomer of "national PARK" which seems to imply that is is more or less a free romp area.

so which is it? where am i allowed to go, what do i need a permit for, and what are the limits of the permit?

also:

how do i know if land is owned by someone or not? if land isn't owned by any private individual, then who owns it? the federal government? if so, what types of federal land can i freely roam on? are there certain types that are off limits and certain types that arent?

please help me, or at least someone link so a quick rundown because i have no clue about any of this.