In my experience: in the 3's & 4's, taking a wheel was as easy as just putting your bars in front of someone else's and kind of edging over, usually they would get out of the way/coast to let me in. (I'm not a big guy fwiw)
In the 1/2's, not so much. 10% of the time that works, but unless it's your teammate you're gonna have to fight a bit harder. This is where leaning on people, banging bars, dive-bombing corners comes in to play. I try to avoid all that as much as possible, since usually you can just wait for a gap to open and fill it - and what goes around generally comes around. If you're constantly pushing people off wheels and generally being an *******, people will know that and it will probably come back to bite you.
But there's a lot of things that make this an 'it depends' answer: how close to the end of the race is it? What kind of race (crit or rr)?
Last lap of a crit and you're trying to get on the wheel everyone wants, good luck with that. Or trying to take a sprinter's last leadout guy's wheel when they have a leadout train going, probably not the best idea.
Anyway, what I try to do is generally not put up too big of a fight, unless it's really worth it. If it's strung out and I want shelter, I'll look for a gap (or half a gap) and slot in. Or if the wind is front the right, maybe you don't need to/want to be in the line, but on the left side anyway. Most guys will let you in unless it doesn't make sense to, or they just don't like you.
And on the flip side, for protecting a wheel if someone pushes me off it, I'll just move up a few spots and slot in if possible. I always hope it makes them feel stupid, like "I didn't want that spot anyway"! But if I really don't want to give it up, and I'm not afraid to tussle with them a bit, the best thing to do is not give an inch. If they move in, move over to push them back out. Give 'em an inch and they'll take a mile.