The first thing we check for is rot. And to do this we take a screwdriver and try to stick it into the wood. If it sinks in easily then the wood is rotten or infested with termites. If you suspect termites then get an exterminator in right away, 'cos as well as eating your deck they will be after anything else wooden that they can find, especially your house.
We start at the bottom and check where the uprights meet the concrete footer. Clear away any gravel or mulch or dead leaves that could hold in moisture. Then get busy with your screwdriver. Check all four sides of the post right down low. Check ALL of the posts, especially that one that is way underneath in the back corner where it is difficult to reach. That is the one most likely to have problems because it gets less sun.
While you are under there, check the tops of all the posts in the same way.
Next check the board that is attached to the wall of the house, Carefully checking at the back and the top where it touches the wall. That's another good place for the rot to hide.
Don't out from under there yet because you still need to check the floor joists, they have a nasty habit of rotting at the top edge of the joist.
Now you can climb out and check the stairs. Make sure that the bottom step is free of last fall's dead leaves and check each step for rot.
Now we can check the topsides, rotten boards here are usually easily seen. If in doubt, give 'em a whack with your trusty screwdriver.
Now let's check for strength. If you haven't dicovered any rotten joists or boards you can safely jump up and down a bit and feel if the is any instability. Be careful when checking the handrailing. You don't want to give it a shoulder charge, 'cos if it is rotten you could find yourself flying through the air. So a gentle shake first and then a little more to make sure.
If all is fine then we can proceeed to the deck surface itself. If you've missed staining it for a couple of years you might find the wood surface a bit rough snd in need of sanding.
For some reason I can seem to find any pictures of decks. This design didn't get implemented as the client decided on a patio instead.