Chain care. What do most people do?

I try and clean and lube my chain about every 300 miles. It might be overkill, but I hate the site of dirt and sand in my chain. Just make sure you arent spraying the chain off with water to clean it without re-lubing it. The chain needs lube at all times.

 I also try and clean my bike every couple of weeks. It takes about 15 minutes with a wet rag and an old toothbrush to get the dirt and grime off the bike.

There have been several threads on this here, here, and here.  Mainly you should be cleaning the chain and drivetrain weekly to monthly, and giving everything a good once over monthly to semiannually.  And get yourself a chain measuring tool to be more precise in assessing chain stretch that needs replacing. 

You can clean the chain with a variety of products out there.  I use Zep (cheap for the gallon at Home Depot) in a chain cleaning tool that scrubs the links as I run it through. SImilarly with lubes there is a broad range.  I like Ice Wax, but it is really all personal preference in the end.  But a clean chain runs smoother, shifts cleaner, and lasts longer.

If you haven't done any maintainance in a year and a half, check the cogs on the front and back for damage.  If there is any, you will need to replace them (as well as the chain).

Oh, and I assume you have been keeping the tires pumped up at least weekly, if not every ride? I can't imagine that they haven't been topped off at all in that time!