Bike Maintenance 101
The first rule to remember is a clean bike is a happy bike. Road grit and grime will work its way into the chain and cogs on your bike and create a lot of friction and noise - not to mention wear out the cogs and chain early. Thankfully, cleaning your bike takes only a few minutes, a bucket of water with soap (bike-specific cleaner or, in a pinch, mild dish detergent) and a brush or old rag. It's a good idea to clean your bike after every ride you do in the rain or on wet roads. Generally, you'll start at the front of the bike and work your way to the back, saving the greasy chain and gears for last. The grit and dirt will come off pretty easily.
Bikes generally require more cleaning in the spring when the roads are wet and may still be covered in grit from the winter.
"Drivetrain" is a fancy word for the chain, rear cogs and the front chainrings, basically all the parts that go into powering your bike forward. When it comes to cleaning the cogs and lubing the chain, things get a little messier than the rest of the bike. We usually use a separate rag for this part of the job. If your bike is very dirty (sloppy spring training rides or getting caught in a downpour on the ride home from work) and the cogs and chainrings are "gunked up" (It's actually a mixture of road grit and chain lube-yum), you can scrub the drivetrain with an old toothbrush and some citrus-based degreaser. You can also use the toothbrush to scrub the small derailleur pulleys as they tend to collect the aforementioned "gunk" too. A major cleaning of your drivetrain is only needed if you can see "gunk" collecting.
Lubing the chain:
Whether you had to do the major drivetrain cleaning or not, it's always good to re-lube your chain at each bike washing (and any time you hear it getting a little noise as dry chains wear out faster). Use a bike chain lube, available at your Schwinn dealer (not WD-40 as it actually tends to attract road grit and "gunk up" chains faster). Lube the inside of the chain as you turn the pedals backwards, then wipe off the excess with a rag. Now your drivetrain is as ready to ride as you are.