Each class can be different.
All of the original classes in the Player's Handbook use the same chart, found on page 29. There are several levels where no power is gained (4th, 8th, etc).
The Essentials classes can be quite different, you have to consult each class to determine when your character gains new powers.
Spellbooks are a bit different, they are detailed on page 158 of the Player's Handbook. After an extended rest, the character prepares the number of daily and utility spells required for their class. When the character gains a new level that has a daily or utility power two new spells are selected for the spellbook, however only one can be prepared after each extended rest.