If you haven't already, get your hands dirty and follow our tips for maintaining your chain:
Wipe down your chain
Get an old rag and wipe all the grime off your chain. It's easy just hold the chain and rotate the pedal and allow the chain to pass through the rag. You should do this regularly!
Now you've wiped all the grime off the chain you need to apply some lubricant to the inside surface of the chain links. One drop on each link will suffice. But before you do so make sure your lubricant is suitable for your riding conditions. If you ride in the wet use a wet lubricant, which is stickier, and if it's mostly dry use a lubricant suitable for riding in dry conditions.
Washing your chain
How often you need to wash your chain and drive train for that matter depends on a number of factors which make it variable. Things like frequency of riding, how often you clean your chain, conditions you ride in etc. You need to make a judgement call but when you see any grime build up I would give it a wash.
When washing ensure you use a suitable citrus based bicycle degreaser and wear appropriate personal protective equipment. Give the chain and drive train a good scrub with an old hard bristled brush. Make sure you scrub the chain, cogs, chainrings inside and out. After this give it a good rinse and repeat the process. How many times you repeat depends on how filthy the chain and drivetrain are.
There you have simple chain maintenance. Whilst this isn't the most pleasant task if you maintain your chain you'll have an infinitely better riding experience and minimise the risk of problems while riding.