for the chain, you can go to your LBS, they should have a little device that measure how much the chain has stretched.
usually, I do it every 6000km (3700mi for the metric challenged).
the cassette, can be chainged every 6000mi or so, depending on the quality.

I've got a POS bike that came with sora components. I'm thinking of changing the gearing and it sounds like I can build my own cassette by buying different individual gears and assembling them on the original cassette body? (I've been looking the at park tools web site). Is this correct? Is this how everyone does it, or do people commonly buy entire new cassettes?

right, every three-four thousand miles or so. but remember, the cassette and chain wear together, so if you wait to replace the chain until it absolutely needs it, the cassette will need to be replaced as well. better to replace a chain every 2000 miles or so, and spend twenty bucks, than 20 bucks plus 150 for a cassette every time.

tommy

Tommy, if you're paying $150 for a cassette, I'd suggest you find a new LBS. You should be able to find an Ultegra cassette for $40-55. Regardless, I still agree with your point.

Entirely agree. Err on the cautious side. I use to live on the Gold Coast in Oz. and saw Jason Shortis a few days after his accident (in 2000 or 2001 not sure)...
his chain was kind of oldish, he pressed hard uphill, the chain snapped, his calf fell back right on the big chain ring (chain on the small) and it tore through his achille tendon...

one detail. if you change the cassette first, then change the chain.the new cassette will use the chain in different spots than the old one and the chain will be more fragile

I agree. Skip using those chain wear indicators. Just replace the chain every couple thousand miles and the whole drivetrain will last much longer and work much smoother. It's like the oil change in your car. Sure, you can push your oil changes past 3K, but it's great cheap insurance that ensures your engine will last a long time. I don't waste the money on expensive chains either. Just a good middle of the road chain will work fine.

It's actually not common to do it that way. Almost everyone buys complete cassettes. If you are going to do it piece-meal, make sure you know what you're doing. There are compatibility and shifting issues to be dealt with.