It's possible the previous owner just sprayed lube on one side and didn't think (or bother) to do the other.
Firstly, put the bike on the centre stand and move the chain up and down, feeling for any tight links (ie where the individual links don't move separately), also, try to push it up against the swing arm.
Turn the rear wheel by hand and do this check all round the chain. If you have tight links, try putting some chain lube on first, making sure you get it on both sides. If you put a piece of cardboard behind the chain and spread a rag underneath you can spray the lube on without getting it on the brakes or wheel. (Personally I use a Scotoiler which put a drop of oil on the chain ever 30 seconds or so and saves a lot of hassle!)
Also put spray some on a rag and rub it over the inside surface where it's rusty. Note DO NOT try putting it in gear and let the engine drive the chain unless you want to say goodbye to your fingers! (Seriously, people have done this...
)
Next, see if you can push the chain easily against the swing arm and hold it there or, alternatively, can't get it to touch at all, then it's too loose or too tight and you'll need to adjust it. The slack should be between 45 and 55 mm. There's plenty of information online about how to do this.
Also run your finger between the teeth on the rear sprocket. If you can feel a "lip" or a "hook", then the sprocket is worn and you'll need to replace both sprockets and the chain. Generally a DID X Ring 520 chain with JT sprockets is a good replacement, you can get them online for about £110 or so.
Hope this helps
PS check for a local Bike Safe, IAM or RoSPA and get yourself some advanced training, you'll pick up a lot of useful information and be a safer and better rider too
