MGD,
Bill Cameron has said most of it. But here's the way that I usually proceed. Like Hank I pick up junk guitars and play at fixing them.

No matter how expensive your guitar there are some things that you should check.
The clearance between the strings and fret nearest the bridge should be about 1/4 inch. If it's any more than that then you would probably get some benefit from lowering the action. File down the bridge insert to lower the action. You might want to buy a new bridge insert and nut before starting. They are very cheap and if you are making a habit or hobby of this you will want to keep one or two on hand.
Before you do that though you need to check that the fingerboard is fairly straight. First sight along the edge, hold the guitar on it's side and look from the bridge end towards the nut. It should be straight, but slightly concave is acceptable. If it's convex you can try adjusting the truss rod a little, but as Bob said, don't do too much. Slacken off the strings and turn the screw no more than a quarter of a turn at a time. Tune the guitar and see if there is any improvement.
Another way to check for straightness is to hold a string down at the first fret then push down on the string near the bridge. The string should touch the frets evenly all the way along.
If everything looks good then you proceed to playability testing.
Problems consist of buzzing of the strings on the frets. Buzzing of bracing under the soundboard. Bad tone, either too dull or too resonant.
For buzzing of strings on the frets first try raising the nut a little. Take the strings off or slacken them and pulll them aside. With a sharp knife pop off the nut, it should separate quite easily. Cut a slice from a business card and place it under the nut to raise it a little (it won't need any glue). String the guitar and try again.
If it's really bad and one fret is obviously higher than the rest. Then make sure that the fret is seated correctly. A little tap with a small hammer will take care of it if the fret has risen out of it's slot. Put a piece of wood or cardboard on the fret before you hit it.
If that doesn't work you can carefully file the fret down with a very fine file or emery board. Just a little at a time and try it frequently.

It's really a matter of observation and experience to know where to start. Take it slowly and have fun. Post any more specific questions here and you'll get lots of opinions.

Bert.