A lot of the times I can figure out the chords to use, but other times I cannot. I've never seen a piece of tablature list the notes as they're being changed, so, how do you figure out what chords to use?
I think it's pretty difficult to guess the chord only by the tab as you don't know the root or even if played notes are within the chords. At most, you could guess the scale by joining the featuring notes, indentifying the major key so you could infer all the possible chords (3 majors, 3 minors and a diminshed) for that key, But that's of course if you are referring to a music not specially harmonically complex (jazz,classical...). In that case:
I would start by ear, virtually all modern songs can be played/sung over with basic plain chords (3 notes - minors or majors). If you played a lot, you have probably developed some kind of sixth sense to know what's the next to come, even on the fly, they usually follow same paths, you transcribe the tension of the change.
After that, I for one try to figure out if a seventh (4th voice, either major or minor) fits in the sound. AS you'll perhaps know, majors are very noticeable (like bossanova for me), and minor sevenths sound to me like a richer minor or with more tensions, less mellow, more bluesy.
Very rarely I feel like I cannot guess the chord. If it's not a diminished or a sus2/sus4, which are fairly noticeable, I try to sing the chord myself, identifying the first note that comes to my head for that chord. I find it in the guitar, and then start finding any ressemblant interval. Then I complete it a bit by hit and miss.
But that's of course, if you can't allow yourself not being 100% picky. EVen if it sounds allegedly perfect, there is always a possibility to not play the same notes as the original artist, or some note being muted by some other instrument in te record, etc..