Cleaning and Inspection
Before you can decide what needs replacing, you'll need to clean and inspect the entire bike for damage. Start with a thorough rinse using your hose's low setting and a soft sponge, and use a citrus degreaser to remove caked-on grime from the chain, cassette and crank set. Then, use dish soap and a soft sponge or rag to polish and clean the frame, handlebars, rims and drivetrain as best you can.
Replace and Renew
If your bike has parts that are caked in rust or corroded beyond use, you'll need to replace them. Many older bicycles use vintage parts, so you might need to enlist the help of a bike expert at your local shop to find things like square-taper cranks, internal hubs or coaster brakes that aren't made anymore. Double-check that the cables, brake pads and tires of the bike are fully functioning, as these can make your bike very unsafe to ride if they're corroded or decomposing. You'll want to fully inspect the entire bike for damage, but pay special attention to the wheels, drivetrain and contact points, like the seat and handlebars.
The chrome parts of your bike can be polished to their former glory. Take aluminum foil and water, and rub down the rims, handlebars, cranks and other chrome parts of your bike. The aluminum foil is softer than steel, so it won't scratch the metal. This process also releases a byproduct that polishes the metal to a high shine. If you've got stubborn buildup on your bike, a little vinegar can help restore the luster you're after.
Before you ride your recently restored bicycle, you'll want to make sure everything is functioning properly and the bike is safe for riding. Your local shop can diagnose any particular issues with brakes, tire pressure, bearings or your drivetrain before they cause you problems on the road. Taking your bike into a bike shop can also give you the opportunity to show off your noble steed to someone who will really appreciate your hard work.