Manuals of [Skill] are rare books which greatly speed the rate at which you train the skills they pertain to by applying a +4 bonus to your skill aptitude for as long as you have the manual in your inventory. You can study more than one manual at a time, but only if they pertain to different skills. Each manual has a limited amount of extra XP they can provide: once that amount is reached, the manual is destroyed.
Manuals essentially generate free experience, and at a rate dependent on the amount you train the skill they pertain to. Pouring 100% of your experience into the appropriate skill will grant you the extra experience ten times faster than if only 10% were going to the skill. However, if this means ignoring other skills that are immediately useful to your character in order to train something you don't really need just yet, using them may actually be harmful.
Users of manuals may want to add this to their Options file Init.txt (see options_guide.txt):
force_more_message = finished your manual
This will alert you when your manual's skill aptitude bonus has run out and allow you to readjust your training priorities should you desire.
Prior to 0.13, you could only study one manual at a time, and you would activate or deactivate them by reading them.
Prior to 0.9, manuals functioned very differently because the skill system was very different. They would allow you to assign stored up experience from your experience pool to a specific skill without actually using that skill, and would crumble to dust after sufficient uses.