For S/C props on single piston engined GA planes, it's generally "The pilot can't get it wrong". If you need to move the prop control, do it gently. If you were to fly, and never touch it, you'd make more noise, and waste some gas, but not hurt anything. There are different systems, but those differences will be transparent to the pilot. With the exception of coursing out the prop in the case of a prop overspeed (generally a result of a maintenance defect), there's otherwise not a lot that a pilot needs to do to keep things within limits.
As always, there are exceptions, but they are rarely found on GA piston singles. If you're flying a GA piston plane which is different, someone is going to tell you, 'cause it's a feature. The example which comes to mind is that a few MT props on piston GA planes have reverse capability (you'll see the switch). That system is foolproof, though reading the flight manual supplement is a good idea!
I understand that some old military planes can be different, I've only flown one. Again, if you're flying one of these, someone will be explaining it to you.
Piston twins are generally the same, other than they incorporate feathering ability. Again, someone is going to explain that to you before you take the plane, however, be sure that you understand the conditions under which you cannot feather. Some props, and I've read it in the flight manual, cannot be feathered if allowed to slow to too low an RPM. Instead of allowing a feather, the prop thinks it's being normally shut down, and blade pitch latches hold the blades in fine pitch. Nice for a normal ground start next time, but a big problem if you needed to feather it for real in flight. Know your plane.
Turbines are very different. If you're flying a turbine, someone is going to explain it to you, during long, costly training. Overspeeds and surges are more easy on some turbines (PT-6's) with careless operation. The test pilot I was supervising while flying a PT-6 yesterday, had trouble getting the rhythm of the power lever, and this resulted in some undesirable prop speed surges and slight overspeeds. Turbine engines have lots of rotational inertia, and prop pitch which moves differently (sometimes below "fine" pitch). So, training....
The bottom line is follow the training provided to you, and move knobs with considered gentleness. Otherwise, don't sweat it, unless the training has told you that you should sweat it!