There are many ways to wash a bicycle. If you Google "washing a bicycle", you'll find different options. Personally, I get a bucket of soapy water and a rag and wash it like you'd wash a car. I use an old toothbrush to clean the dirtiest and hard-to-reach parts, such as the chain, gears, jockey wheels and derailleurs. I use Simple Green as the cleaner, but you can use almost any detergent. I rinse the bike off with a hose without a spray attachment.
You could use 3-in-1, but I'd recommend visiting a bike shop and picking up a bottle of lube specific for bicycle chains. If you're a cheapskate, you can make your own out of a mixture of motor oil and mineral spirits--Google will help there too. I don't recommend starting a discussion of lubes, as such discussions always go on forever and everybody recommends something different.
You might consider cheap furniture polish (e.g., a "Pledge" knock-off for about $1 a can) to shine up the tubes.