This is one of the most common questions I see in Swtor so I decided I'd put cheapest swtor credits together a guide on it! Players are able to Respec (Reset your talent points, in other words) in two places. The first will be your factions fleet station and the second will be your factions main planet. So Coruscant for Republic players and Dromund Kaas for Imperials. This guide will cover the Fleet Station Respec guy whom is located in the Combat Training area of your Fleet Station. The location will be different on the Imperial Fleet Station (maybe) but from my experience the Respec guy is in one of the "last bins".
You can see what I mean by "last bin" in the picture. What I mean by that is one of the rooms on the end. You'll know when you see him because he is labeled as the <Skill Mentor>. Once a week players will be able to respec for free but after that it will start costing Credits. It won't cost much at first but the more you respec the more it will cost. I am not sure if the cost resets every week, I'd assume it does but I have not tested it myself or heard from anyone if it does.
Another thing is, unlike other games every class will be speaking to the same NPC to reset their points. That means don't go snooping around your class trainer looking for your respec guy (I did this for awhile, felt pretty stupid once I found out who we really talk to). Anyway, here is a picture of the guy you will be speaking to on the Republic side to reset your talent points.
That's about all there is to know about respecing. Maybe in the future I'll put up a map of the location on Coruscant/Dromund Kaas as well as the location on the Imperial Fleet Station. If not, just look for the <Skill Mentor> in the Combat Training area on the Fleet Station or the Crew Skill/Auction House area on Dromund Kaas/Coruscant.