Your chain is easy to keep in good shape and a potential nightmare if you don't. Neglect it at your own risk!
Despite the surface rust and ill-kept nature of some chains, it's worth trying to resurrect it but first you're need a racestand or you might be blessed by having a motorcycle center-stand. If you've got it, use it. You can make do with a friend and a sidestand out on the road, but it's tricky and less than satisfactory if you want to do a proper job.
Identify the sort of adjustment you motorcycle uses clean and lubricate it. A penetrating oil may come in handy... Note the reference marks for wheel alignment. They may be accurate, but it's worth string-lining your wheels (2W04/10) to make sure.
Search for and identify the joining link your chain uses in case you do have to replace it. Our chain has a riveted joining, most chains have a circlip. If you can't find any join, you may have an endless chain, and that means you need to remove the swingarm for replacing the chain.
Using a CFC-free spray pack of the right chain lubrication for your chain and the extension nozzle, direct a dribble of spray to the inside of the sideplates. This is where the lubrication has to penetrate. As you spray the lubrication on the chain, turn the rear wheel with your other hand so that the chain moves away from the nozzle. Continue until the whole length of the chain has been lubricated.
Don't overspray because you'll just be cleaning the mess off the back of the motorcycle if you do. Repeat the other side of the chain link. Allow a bit of time before you ride again for the lubrication to sink in.
Once you have removed the split pin and have the right spanner/socket for the job so that you don't get stranded mid-operation or round off your axle nut, loosen the nut so that the axle can move fore and aft.
Check the chain halfway along its bottom run. The measurement will be in your owner's handbook. Turn the wheel, check for tight spots and measure at the tightest point.
Ter turn at a time, repeating on the other side to keep the wheel straight. Check the chain tension often. Once satisfied tighten the locknuts, make sure the axle is seated against the adjusters and tighten the axle nut and refit the locking pin. Recheck all nuts, and you're ready for a ride...