First, what you will need

Processing tank--I use a Paterson 3 reel tank
Reel--I find the Samigon easiest to load
Thermometer. Any is fine really
Developer
Stop Bath (not completely necessary, but very useful)
Fixer
Photoflo (also not necessary, but almost essential to prevent water spots)
Film Clips for drying (I use chip clips and paper clips)
A sink and running water
Changing bag or dark room, film has to be loaded on the reel and into the tank in complete darkness

Here is a massive chart for varying developers/films, very useful. 

I suppose first step is actually mixing your chemicals as indicated on the package. 

Let's Begin

1. If it's 120 film, prewash with water at 68 deg for 1 minute, otherwise go straight to developing phase for 35mm film.

2. Pour developer in dev tank. Should be 68 degrees (You can develop within 64 and 77 degrees by using the Ilford Compensation Chart). Agitate continuously for first 30 seconds, and then for 5 seconds every 30 seconds afterwards.

3. Pour developer back into jug when there's about 10 seconds remaining.
(the only time you don't want to reuse developer is when you're mixing at a ratio, like 1+25 Rodinal, etc.)

4. Immediately pour stop bath into dev tank. Agitate continuously for 30 seconds to one minute, then return to jug.

5. Pour fixer in dev tank. Agitate continuously for first 30 seconds, and then for 5 seconds every 30 seconds afterwards. I fix for 5 minutes Return to jug.

6. Final rinse. Just like the first wash, but do it 10 times. Either this or fill dev tank with water and let sit for 10 minutes, then pour out.

7. Photoflo - let sit in dev tank for 1 minute, then return to jug.

8. Remove film from the tank, and run a film squeegee or fingers (I use my fingers) to get excess water off, then hang to dry for 2-3 hours. Should be in a less humid dusty area. People seem to use their showers. 

Some examples of my at home developed photos.