If you really want to do a "pro" job, you need to cut the bottoms of the vertical door casing trim where they meet the floor, just enough so the new flooring slides under them with a snug fit. (This is assuming they are already low enough that the flooring cannot slide under them. If they're already too high, don't worry about it now.)
You can do this 2 ways: Buy an undercut hand saw (sometimes referred to as a Japanese butterfly saw), or rent a jamb saw. The hand saw is tricky to use, so practice using a piece of wood that is thinner than your flooring, and make a couple trial cuts to your casings. The hardest part about using it is keeping it cutting straight, especially since you're down at floor level, on your knees. Oh, it's also called a "pull saw", in that you cut with it by only pulling it toward you. Be careful; it's very sharp, and can easily cut you just by brushing it carelessly against your hand. Tack a small piece of your flooring to the floor, then rest the saw onto the flooring, keeping it flat against that scrap piece, and take your time. Technically that scrap piece needs to be just slightly thinner than the actual flooring, to account for the thickness of the saw blade, which in my experience can sometimes be accomplished by removing the padding from the back of the floor (if it's that type.) Otherwise, getting that cut just right might be too much trouble, and having a small but of extra wiggle room will probably work in your favor anyway.
A jamb saw is a special type of circular saw that lays on its side, and can cut those casings quickly, accurately, and at the exact height you need so the flooring will slip under. Again, be careful. Watch some videos, and get the guy at the rental store to show you how to use it.
Either method, remember it's like cooking a steak for the first time. If you're not proficient, just remember you can always cook it a little more, but not less. Same with undercutting door casings. If you cut them too high, you'll have a gap. Too low, just adjust the saw to cut a bit higher.
With the jamb saw, once you have it adjusted so that it makes the correct height cut, you just leave it there, and cut the remaining casings. Just make sure it is sitting down on the subfloor, and not, for example, resting on a nail head that's sticking up, or the saw may cut too high. If you're not familiar with using electric circular saws, you may want to pass on this, or find a carpenter who can help. Actually that's not a bad idea anyway. Your call.
That's the prep. Lots of details huh? Oh, and if you have any squeaks in the subfloor when you walk around the room, now's your only chance to fix them. Get some 2-1/2" screws and add them wherever it squeaks. Make sure you hit the joists below, which are every 16" or 24" from the 4' edge, measured perpendicular to that edge. (You should see the existing nail locations to help you find the joists.) Sweep and vacuum the room. Well.