A basic safety/maintenance check includes the following:
1) Air: Check your tire pressure before each and every ride. This comprehensive guide explains everything you need to know about tires, pumps, valves and pressure.
2) Brakes: Make sure they are working properly, and that everything feels normal when you squeeze the levers.
3) Chain: A clean, lubed chain is a happy chain. Your drivetrain will run more smoothly and you'll save wear and tear on your components. Pro tip: For the best results, clean and lube your chain the night before or several hours before you ride.
4) Thru axles/quick releases: Double check that these are tight and closed properly. Learn more about axles here.
5) Dropper post: Make sure it extends to its full height and drops down when the lever is activated.
6) Suspension: Wipe fork and shock stanchions down, pedal around, give your bike a good bounce and make sure everything feels normal.
7) Shifting: Run through all of your gears to ensure they're all working properly.
Be sure to have your bike and suspension serviced on a regular basis to keep it running smoothly and catch small problems before they become a bigger issue.