You want to give them a visual inspection looking for anything that shouldn’t be there, (e.g.:brown rust marks, salt erosion). Then run them through two fingers feeling all the metal work for rough surfaces as these will damage ropes/slings. When you’ve done this do up the screw gates to make sure they do up and give them a click check, (press to make sure it won’t open), unscrew and do the same, this time hope it opens!
Wire gates same as above but make sure the gate is still springy and no bends or damage to it.
Any karabiners that have wear thinker than 1mm need to be considered for retirement.
Give all ATC type devices a visual check looking for anything that doesn’t seem right, (cracks, chips, erosion). Feel around the head of the device where the rope rubs to make sure that there are no sharp edges, and wear isn’t too great.
Grigri’s you want to give them a wipe inside with so tissue to get the built up fibres out. Then check for sharp edges where the rope runs and make sure the front opens and closes smoothly on its pivot. You also want to push the handle part forwards to make sure its still smooth and doesn't stick.
Figure of Eight:
Same checks as above for ATC.
Same visual check, then you want to check the cables, if they are visible as on the DMM dragons for any damage. Moving down the cam you want to make sure it has a smooth action and that all the lobes move as one. Checking the slings the same as for Hex’s.
This is just a guide as to what I check. I do not accept responsibly for any damage or injury resulted from following it.