1) Do not shave every day.
2) Soak the place you are going to shave in hot water (like take a bath) for about 15 minutes before shaving.
3) Use a very good quality razor, such as a Mach 3 Turbo.
4) Good razors have strips on them to stretch the skin out before the razor hits the hair - this reduces razor burn effect. Be sure to not press to lightly or too firmly with your razor.
5) A good shaving cream is hair conditioner, it's nice and slick. Rub it on against the grain of the hair.
6) After you finish shaving, apply a generous amount of witch hazel (you can buy this anywhere you can find bottles of isopropyl alcohol. Use this as your "after shave". It will work wonders to minimize razor burn and any other ill effects.
As a side note, if you are female and prone to UTI (urinary tract infections) or yeast infections, try shaving your pubic hair off completely for a few weeks and see if it helps.
For males specifically, you'll want to stretch and contort your skin with your hands by pulling and tugging until it is flat and taut before you run a razor across yourself. The hardest areas on males that I am aware of is the hair at the base of the shaft on the top. The hair growth here is thickest and the angle you hit is quite difficult to shave at. If you are shaving here, pull down on the shaft at an extreme angle and shave downward, if you shave up you are very likely to get nasty razor burn. If you are pulling down very firmly though when you let back up the hair you thought was there will have retracted back into the skin and it should be smooth to the touch.
Sorry maybe it is a bit difficult to describe in text. =)