Gortman,
There is currently a bug (at least in the enhanced client) where in the balloon text you don't see the complete skill purchase offer. You have to look at the Journal to see the whole statement. There it will show how much gold he charges for the training. The cost is always 1 gp per 0.1 skill point. So if he is going to charge you 345 gp, you will buy 34.5 skill points. Most of the trainers in New Haven will let you buy skill up to 40.0. So in my example, you would have already had 5.5 skill points.
To actually pay him:
1) stand close to skill trainer
2) ask him about training the skill you want
3) drag that much gold onto him
You should then get a confirmation statement saying that such-and-such a skill went up. If this doesn't happen, you either missed him when you dragged the gold, you are at your skill cap, or the skill in question is not set to go up.
Also, once you accept a skill quest, you can't purchase any more skills. So if you want to train multiple things at once, get all of them bought first, then start accepting the quests. For example, a new warrier might want to do the accelerated skill quests for:
* Swordsmanship
* Tactics
* Healing
* Anatomy
* Parry
* Focus
* Chivalry
He should buy all to 40 first, then get the quests. If you already accepted one or more quests, then realize you should have gotten another one, you can drop all the skill gain quests you have, purchase what you need, then re-get the quests. There is no penalty.
Note that not all skills have accelerated skill gain quests. These include tailoring, all bard skills, and alchemy. Also, a few skills do have a quest, but you can't buy up to 40. One of these is inscription, which you can only buy up to 33 or so.