The Wiki has a lot of example circuits with pictures.
You might be better off starting with a step by step tutorial but when you feel ready to move on you could try building a few of the circuits in the Wiki and experiment with conneting the output of one to the input of another or altering them a bit and see what happens.
and then follow the links to more specific functions.
And, of course, asking here if you want to know how to do something specific or want to understand why your circuit doesn't work.
Screenshots are very useful for seeing where you might have put a repeater in backwards or something.
More complex builds may require a world download to test.
Speaking of which, if you search through the forum you should be able to find links to world downloads of interesting builds like piston doors and such. Though there will probably be a lot where the links no longer work of course.