If you're staying at Disney World Resort hotel, you can book book your Fastpass+ 60 days before you check-in date. If you're not, you can book your Fastpass+ 30 days before.
Either way, you'll need your My Disney Experience account, and have hooked up your holiday or tickets to do so. After logging in, scroll down and you'll see your booking options, as shown below.
The Fastpass+ padlock icon will disappear when you can start booking your Fastpasses.
General FastPass+ Rules
You can book up to 3 Fastpasses per day.
You can only book Fastpasses in one park (can't have 2 in Magic and 1 in Epcot, for example).
On the day, if you have used all your previous Fastpasses, you use the My Disney Experience app or kiosks in the park to book another.
You choose a one hour window that's available. Don't miss it!
Booking your Fastpass
After you click on the 'Make Selections' link, you first choose which park you'd like to book your Fastpasses, and then which day. You can then choose up to 3 attractions within the time frames they offer.
Fastpasses are not set in stone when you choose and confirm them.
After you have chosen your Fastpasses, you can go back in and edit the times or attractions afterwards, if at first the time you really wanted wasn't showing up.
(One thing to note is some parks have tiers, which stops you from booking Fastpasses to all the big rides in each park. For example, in Epcot, Soarin' and Test Track are on the same tier list, so you can only Fastpass one of them for that day.)