They can also be burnt in a fire as a consumable, but this is not recommended incase you wish to revisit the same world if your character dies.
Using Skill Books
Put the skill book in your main inventory.
Right click the skill book and click "Read".
Wait for the progress bar to finish.
Double check that all pages have been read (sometimes anywhere from 1-20 pages of the book will not have been read). If some pages have not been read, repeat step 2 & 3.
Check your character's "Skills" page to verify you are now getting a boost to the appropriate skill. (There will be sequential arrows running from the skill name to the skill boxes and hovering over the skill box that is currently being worked on will show the multiplier that is being given.)
Note: If at any point you are interrupted during reading, you do not lose the pages you've read; you can resume where you left off. So don't be afraid to kill a zombie or tend to your garden and then return to reading. The total amount of pages read so far will show up in the book's tooltip when hovered over. Depending on your situation, it may be best to spend a few hours a day (usually at night) over several days working through a skill book rather than attempting to read one straight through in one sitting (boredom, hunger, thirst, and unhappiness will all accrue while reading).
WARNING: If your character says, "I don't get it" or other similar lines above their head, you are reading an incorrect book for your level. Even if you read the whole book, nothing will happen. Make sure you are reading the book that corresponds to the level you are currently working on (Beginner = Level 1 and 2, Intermediate = Level 3 and 4, Advanced = Level 5 and 6, Expert = Level 7 and 8, Master = Level 9 and 10). You cannot read books early.
Skill Book Benefits
Reading a skill book even partially will give your character a multiplier on any points gained for a given skill. For example, if sawing wood normally gives 3 XP and you've read all of the level 1 (Beginner) skill book, you will now gain 9 XP each time you saw wood until you reach level 2. This will dramatically decrease the time required to learn a skill. In most cases, it is not worth wasting resources to grind out a level in a skill unless you have fully read the skill book and have the maximum multiplier.
Higher-tier skill books have more pages and take longer to read. Upon accruing enough experience to finish that skill level (even if you don't use a skill point to level it up), the multiplier is removed and experience gain returns to 1.0x until the next proficiency level book has been read for that skill. You can have as many active multipliers as you want simultaneously (i.e. four skills being boosted at the same time).
Beginner - x3
Intermediate - x5
Advanced - x8
Expert - x12
Mastery - x16
Skill Book Item List
Carpentry for Beginners
A basic Carpentry skill boosting book meant for first-time carpenters. 220 pages long.
Carpentry for Intermediates
An intermediate-level Carpentry book that teaches more difficult concepts for experienced carpenters. 260 pages long.
An advanced Carpentry book that teaches complex concepts meant for learned carpenters. 300 pages long.
A highly advanced Carpentry book meant for exemplary carpenters. 340 pages long.
A Carpentry book meant for adept carpenters. 380 pages long.
Cooking for Beginners
A basic Cooking book meant for new cooks. 220 pages long.
Cooking for Intermediates
An intermediate-level Cooking book meant for cooks with a small degree of experience. 260 pages long.
An advanced Cooking book meant for experienced cooks. 300 pages long.
A highly advanced Cooking book meant for exemplary cooks. 340 pages long.
A Cooking book meant for adept cooks. 380 pages long.
Electricity for Beginners
An Electricity book for new electricians. 220 pages long.
Electricity for Intermediates
An Electricity book for electricians with some experience. 260 pages long.