Thank you! So once I get to the desired altitude, I should set it to a certain power setting, then adjust elevator trim so it flies level with the yoke centered? What power level should I set it to?
In a normally aspirated (meaning there is no turbo/supercharger) piston airplane, with a fixed pitch prop, in most cases, you'd:
Takeoff:
1.) Throttle smoothly to full power
Climb:
1.) Throttle is still set to full power
2.) Set your pitch to maintain whatever climb airspeed you want, typically Vy (or higher if needed for cooling).
3.) Trim to eliminate any yoke pressure, the airplane should continue to maintain your desired climb speed with your hands off the yoke
Cruise:
1.) Throttle is still set to full power (where it remains)
2.) Push forward on the yoke, while adding some nose down trim, trying to get to where the airplane maintains altitude with your hands off the yoke. Note: A good pilot can quickly stop the climb, but the airplane will continue to accelerate, and as that occurs, the pilot will continue to add nose down trim. Eventually everything balances out, but it can take a minute or two.
In most fixed-pitch normally aspirated airplanes, by the time you get to your cruise altitude, the airplane will not be capable of exceeding red-line RPM (or anywhere near it really) at full power (the air is thinner). Because of this, you do not typically do anything less than 100% throttle until at some point in the later stages of the descent. There are things to do with the mixture in these various phases, but, I am lazy and didn't bother to write it.
Also note that you do not attempt to achieve any speed in cruise - you get the speed you get. In the real world, that speed is never as fast as you'd like, so you sit there thinking about how if only you made 50% more money you might be able to afford to go 10% faster! Drag is an unfriendly bastard who doesn't maintain any sort of linear relationship with money.