Here is what I do to clean my car:
Interior:
I have a shop vac that has a couple nozzles on a hose that I use for vacuuming out the car. Shake out the floor mats and move the seats back and forth to get all the crap under them. I just use a wet cotton t-shirt and a bucket of water to clean the interior - chemicals can cause cracking on interior plastic and vinyl pieces. If you've spilled a drink in your cup holders, just soak it with some water then wipe it out with your t-shirt. The shirt also acts as a duster when you do your dash with it. Don't forget about the trunk!
Washing:
Hose
Soft cotton towel
Soft cotton t-shirt
Bucket
Foam scrub brush
Chamois
Squeegee
Begin by spraying the whole car so it's all wet. Start washing from the top down so that all the crud will wash down the car to the ground. I just use plain old water because I don't like washing chemicals eating away at my car. Use the soft cotten towel to scrub the car's body. The most important rule when washing is to always keep the water flowing where you are scrubbing. Paint is easy to scratch and if you get some dirt particles trapped under your towel and keep scrubbing, it will scratch the surface like sandpaper. Just hold your hose above the area where you're scrubbing to keep the dirt moving.
For the windows, use a soft cotton t-shirt, I've found that these work the best. I don't use Windex or other glass cleaners because they eat away at the rubber weather stripping on the windows. Water also dries nice and clear and doesn't leave streaks. You can use the bucket for when you're washing the inside of your car's windows. For the rims, you can use a towel or scrub brush depending on what kind of rims you have. Mine are just plastic rims so a towel or thick foam brush works fine. I usually use a brush because it gets caked-on dirt out better and doesn't gunk up as quickly as a towel does.
To dry the car, use a chamois cloth. It's a special water-absorbent cloth kind of like a sponge...you can scoop up lots of water with it and then wring it out. It's a very quick way to dry your car and prevents water spots. For the windows, I just use a squeegee. For cleanup, it's nice to use liquid fabric softener on the towels and shirts like the tutorial in the link a few posts up says, that way everything stays nice and soft. Make sure the windows aren't frosty when you're done. Also give the headlights, tailpipes, and license plates a good scrubbing. If you have any road tar or nasty bugs that won't come off, you can buy clay bars and bug remover juice from any car parts store.
Waxing:
Wax (I like the Turtle Wax paste in the green plastic can, comes with an applicator)
Applicator (comes with some wax, otherwise available as a soft foam or cloth disc)
Painter's tape
Shady area to wax your car in
Soft cotton towel -or- buffer tool
First move your car into a shaded area, like under a tree or carport or in a garage. The reason for this is so that the wax won't dry too quickly. The basic idea is to wax up a section of your car using the applicator, then wax up a second section, then go back and buff off the wax off the first panel using the towel or buffing tool. After that wax up a third section, then go back and buff off the wax off the second panel, and so on. I really like the idea of using the blue Painter's tape to tape off edges the trim pieces; it's a real pain to get wax off little plastic crevices. Alternatively you can just wax really close to the edge, but try not to go over.
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That's pretty much all that's needed to keep your car shiny and clean. How often you do it is up to you (i.e. if you have kids you probably want to vacuum it out weekly). You can buy plenty of aftermarket cleaning products, but I've found they don't really do much for you. You may also need to pick up some specialty items like chrome polish or tire shine depending on what you have on your car and how you want your car to look.