I generally start by booking them on my computer using “My Disney Experience.” Start by making an account if you don’t have one, then “link” your traveling party to your account.The site will guide you. You’ll need to enter your tickets as well (you can’t do FP’s until they know you have tickets).
When you go to choose a FP, it will ask you if it’s just you needing the FP or other people in your party. You choose the attraction and it will give you available FP times. The site will let you know what’s available and what things you can choose at the same time – some things are categorized so you can’t get more than one from a category - but the site will help you do that.
Once they’re in, you can also “modify” them, so nothing’s in stone.
We use the app to keep track and send us reminders. It will also let you know if a ride is down during your FP window, in which case you get alternatives. The app ties to your ticket / magic band, so you just scan it when you get to the FP line for the ride.
I’m sure there are some great blogs out there with more info, but at least that’s a start!