Trainers can give you the ability to learn new skills, or raise the level cap of the skills you already know, but you still have to put skill points into any skills you wish to use.
For example, near the start of the game Fergus drops a book that teaches the Identify Equipment skill up to level 2, so you can have one character learn it (using 1 or 2 of their skill points). In order to learn higher levels, you must get the cap raised by a trainer. In this case, the weapons officer in the drill grounds later in act 1 teaches Identify Equipment up to level 5 (as does the temple smith in act 3), while Brian in the act 4 BF teaches it up to level 10.
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