I believe there is a sticky FAQ that talks about it. In a very brief nutshell:
When you're looking to make a new FP+ click on the attraction you want. If it's not available, you literally refresh the screen by clicking on a time at the top of the screen (if you have an Android you can click the same time over and over, Apple you have to pick different times). If it is available, but not for the exact time you want, take it and then follow the step below.
If you're modifying a FP+, it's pretty much the same thing. Pick the time you want, if it isn't available, click it (the time, based on Android or Apple as above) again.
Rinse and repeat until success is achieved. Get on attraction and enjoy.