The Remote
Test with more than one known-good remote, fresh batteries, and the correct security settings.
It sounds obvious, but it is always wise to have multiple functioning remotes with fresh batteries.
A remote can fail or become intermittent, so consider the investment in extra remotes as not only a convenience, but also an important troubleshooting tool.
Start with known-good remotes
The point is to always confirm that the malfunction is not being caused by a faulty remote by testing with at least one other remote that was known to be working.
Once that has been checked, further troubleshooting can help isolate other component failures or remote-related problems.
Programming and security settings
Completely dead or non-functioning remotes can lead one to the conclusion that the problem is the remote receiver, so it is always important to make sure the remote has fresh batteries. Sometimes reprogramming the main control board for the remote security setting will get the system working again.
If this is a new system that has never worked, it is absolutely and fundamentally important to program the main control board for the remote DIP-switch settings and confirm that the signal is being received, as described in the receiver section.