Okay, I've done a little more research, and a little tinkering, and now have more specific questions. As I said, the action was quite high, so I checked the neck relief and found a fair amount of bowing. I tightened the truss rod a quarter turn, but was getting a fair amount of resistance so I didn't go any further--don't want to do any damage to it. Then I lowered the saddles quite a bit to get the action as low as I could without messing with the truss rod anymore. So now I have action that is a little too high in the middle due to bowing, and notes choking out on the higher frets (12th and above) because my saddles are too low. I can easily raise the saddles, but of course that makes things even worse in the middle.
I tried measuring the neck relief as per the instructions in one of the tutorials I used, though I don't have the suggested tools for the job. I fretted behind the first and just after the last fret, and measured at the 7th fret. Using a standard ruler, I came up with about 1.5 mm. This is the current state of the instrument (not what it was before I adjusted the TR). Can anyone recommend any steps from here? Or should I just take it into a shop? Thanks.