What you really need to know about is trim. The wheels, buttons, etc are just a way of correcting the trim.
When an aircraft is in flight (no autopilot....manual flight), at any given angle of attack (or speed), you want to be able to let go of the controls, and have it stay in the same position. You don't want to have to continually apply any control input to make it stay where you want. I'm sure you've all driven a car with a poor wheel alignment, that constantly wants to pull one way or another...imagine in you could correct that 'pull' with the flick of a switch.
Aerodynamically, a stable, in trim aircraft, can be disturbed (be it a little bit of bank, or a pitch or yaw change) and it should, with no pilot intervention correct itself back to its original situation.
If, for instance, I'm in level flight at 250 knots, and I reduce the power to that required for 200 knots. The aircraft will start to slow. The tail will no longer be providing sufficient down force to hold the pitch attitude, and it will pitch down. It will no longer be in level flight, but will try to give that same angle of attack, so it should end up in a stable 250 knot descent. Now, if that's not what I wanted, but rather level flight at 200 knots, as it slows I'll have to slowly pull the nose up until it stops decelerating and I reach the pitch attitude required for 200 knots. If at any point, I relax the back pressure, it will again head back to that 250 angle of attack...and as I don't want that, I'll have to trim the nose up. That's accomplished by the pitch trim, which in most larger airliners is done by moving the entire tailplane to a new angle of incidence.
Roll and pitch trimming is generally accomplished by putting a bias into the ailerons and rudder.
All of these only work at one particular speed and power setting. Change anything, and the aircraft will need to be trimmed back to that hands off situation. In an airliner, roll and pitch trim are not used all that much, unless you have an engine shut down, and which case any change will require large trim changes in all axes.
FBW aircraft automatically pitch trim, so it isn't something we use at all until back in reversionary laws.