1. Sharp (new) razor
2. Not too hot water... shaving in the shower is best.
3. Pre-wet and cleanse really good first then lather with a beauty soap like Dove.
4. Put arm as high as possible..grab the shower rod if necessary
5. Hold the razor more vertical to the skin than you normally do.
6. Stroke in whatever direction you feel the hair laying. Reverse direction and cut again.
7. Re-soap and test with your other hand to see if there is any stubble left.
8. Re-shave as necessary..but keep the pressure down..and of course, do NOT hurry!
If you shave nearly every day for a short time...like a month or so, you'll find that you will not get razor burn or red patches on your skin. This applies to pubic shaving too. The skin will accustom itself to the treatment and you'll see less and less rash after a while.
You should use a shaving cream..but the facial "beauty soaps" are pretty good if you have cleaned the skin good enuff first. (Jergens, Dove, etc.) Try to stay away from the health-type soaps. They don't have the essential (read: animal) oils in them.
I like to use LAVA..don't laugh..it will ex-foliate like nothing else and removes blemishes better than most other soaps and palliatives.
You'll notice that the first few times you attempt shaving a new area..it'll protest and rash up on you. Just stay with it and things will mellow out in a short time.
Summer's coming and the bikini line needs some more careful shaving..but start early enuff in the season so that the skin gets used to the treatment and you'll not have any embarrassing rash when you go out in that new Brazilian thong.