This particular drive train has been on my bike for around 7,500 km and has finally gotten to the point where I'm getting phantom shifting. And it's spring so what better time for a little face lift.
To be sure that any problems you may be having are due to a worn drive train, the first thing to do is check for chain stretch. The easiest way is to use a chain checker like the one pictured below. Note that it reads 1.0 in the little window to the left. It actually would have read more stretch than that if the tool went further but once it's at 1.0 it's time for a new drive train. Since the chain and cassette wear together it's always a good idea to replace both at the same time.
These tools are a bit pricey for what they do but very handy. You can always take it to a bike shop and have them check it for you.
The process is fairly simple and involves more cleaning than anything but you will need a couple of special tools to remove rear cogs.
The rear cogs are attached to the hub in one of two ways. Newer bikes tend to use a type of hub assembly called a cassette. Cassette sprockets slide over splines on the hub. A lock-ring threads into the hub and holds the sprockets, or cogs, in place. Older bikes may have a large external thread machined into the hub. The cogs and ratcheting body assembly, called a freewheel, threads directly onto the hub. You'll need to determine what style of hub you have to get the right tools for the job.
In the end the hammer was needed to "assist in turning the removal tool" and the vice grips were needed to yank the damn tool out of the hub again.
New cassette and chains (you need two chains and about 1.5' more for a recumbent).It's all assembly work from here. Use a chain break tool to remove the old chain put on the new cassette and chain and voila! Ready for another 7500 kilometers.
Just in case you're wondering, the strange looking bits on either side of my axle are Bobnuts fixed to homemade extensions to attach my Bob trailer. Due to the Sram Dual-Drive hub that has a click box on the drive side I can't use the standard Bob skewer to connect my trailer or simply attach the Bobnuts to my axle. But that's another post.