Take out the bolt carrier and look at the gas key... the little tube thing pointing forward on top the carrier (if you don't know the parts you need to study some). The gas key should not be loose and the bolts that hold it down should be staked (have punch holes around edge of bolts to help lock them in place). Check the hole in front of the gas key for wear, and you can try to see if the gas tube inside the receiver is worn. Uneven wear might indicate gas tube misalignment and maybe loose barrel nut. A gunsmith will be needed to fix this (it's not a major job).
Check the face of the bolt for dirt buildup and traces of brass shavings. Check to see if the ejector and extractor are clear and functional. Look at the bolt locking lugs and in the chamber for broken or worn lugs. Dirt is the enemy here and the extractor is subject to damage and the spring lose tension. These can easily be routinely corrected. The gun will tend to fail to extract empty case and cause jams.
Check that where the stock connects to the receiver is tight. You may check that the lock nut (castle nut) is staked to the plate between it and the receiver. The bolt carrier gets pushed back into the buffer tube in the stock when fired so you do not want the thing to come loose. If you can take out the buffer and spring from the tube in the stock you can check that it isn't unevenly worn or damaged. You need to learn disassembly of these things, which can be found on Youtube.
Here's something that you can check if you'd like. Check the function of the trigger and safety (do not dry fire the gun with the upper and lower separated). Of course the thing shouldn't fire on safe. Cock the gun, pull the trigger and hold it back. The hammer should have struck. Then, while holding the trigger back, pull back on the charging handle as if to cock the gun. The hammer should be captured. Push the charging handle forward to lock it. This is the disconnector capturing the hammer to hold it back until the trigger is released. This prevents misfires. Slowly ease the trigger forward until the gun makes a slight click sound. This is the disconnector releasing the hammer which then should be captured by the trigger sear. You should then be able to ease the trigger forward all the way and then pull it back to fire the gun again. If the hammer gets released when you eased the trigger forward you might have a timing problem in the fire control system which can cause multiple shots. It's tricky though and you have to be careful because the point that the disconnector releases and the sear engages is so touchy any unsteadiness or tremor of pressure on the trigger can fire the gun. If it's out of time a gunsmith will be needed to fix it (it should be fairly simple).
I think that's most of the main stuff. If all this looks good then clean it, lube it, and head to the range. First place only one bullet in the magazine and fire it at the target. The empty should land at an angle to the right and behind you. Recover the empty (let it cool before picking it up with a bare hand) and look it over carefully for deformity, primer perturbing out of base, or damage to the case rim. If the case throat is flattened it was caused by it striking the shell deflector. If all this looks good the headspace is probably OK. Load several cartridges and try firing sequentially, load a few more and try rapid fire, and if all goes well and all the empty cases look OK load the magazine, sight her in and enjoy. Failures to feed with multiple magazines are probably caused by the bolt carrier not going back all the way, likely due to a gas key or buffer issue. Jams can be bad mag lips or extractor/ejector issues, though you might check feed ramps.
