Paul,
Here are some methods I've found useful, and they vary according to whether the plane is a bench plane or a moulding plane. To set the initial blade depth on bench planes, take a straight stick of wood, narrower than the blade, say 1/2" wide, fix it in a vise or on your benchtop, and balance the plane on it. Lower the blade until it rests on the wood, and work it side to side feeling the camber on the blade, until you're satisfied that the blade is about right laterally. Then with the blade lightly resting on the stick, slide the wedge in, and set it finger tight. Push the plane forward just a bit and if the blade feels about right, give the wedge one tap with a wooden hammer, and that should set it pretty close. Now test the blade on the stick of wood, checking that the shaving is thickness you want, and that it's the same thickness if you plane on the left side as on the right side. If not, take your hammer and tap the blade on one side or the other to get the lateral adjust right.
To set the blade deeper, tap down on the blade, then on the wedge--tap, tap. To raise the blade a little, but not take it out, tap with a wooden hammer forward of the blade on the plane body--this should raise the blade, but leave the wedge in place. So you tap forward of the blade, then tap the wedge to reset it--tap, tap. After some practice, you get an idea of how hard to tap forward of the blade to get a certain increment of blade raising. Many longer planes--try planes, jointers--will have a strike button installed for this purpose. You can easily install your own strike button from scraps of dense wood you happen to have on hand.
To remove the whole blade+wedge assembly, take your wooden mallet and hit the plane on the rear strike button, or if it does not have a strike button at the rear, on the upper rear edge, at roughly a 45-degree angle.
Now on moulding planes, the initial setting of the blade is best done by eye, since you must set both the depth and also set the blade profile to match the bed profile. Turn the plane upside down, and sight from front to back. Practice this til you get the hang of it. On a moulding plane, I like to use a small wooden hammer to remove the wedge by tapping on its finial, or if the blade is snecked, on the blade. You certainly can remove the blade by hitting the plane at the rear, and you will see lots of hammer tracks on moulding planes from people nailing them with steel hammers.
If you're gonna be using woodies a lot, a very useful tool to have is a hammer, say 8-10 oz in weight, with a brass poll on one end of the head, and a wooden poll on the other. The brass poll will not mushroom the blade when tapping it in, and the wooden poll will not make tracks on the plane body when raising the blade. There are commercial hammers of this type available, or you can make your own, or you can improvise with what you already have to hand.
There are undoubtedly a number of ways to perform these adjustments. Some people have the ability to feel the right blade depth with their fingertips, for example. After you do it for a while, you will develop your own methods which are efficient for you.
Woodies are a great adventure!
Wiley