If you're having trouble shaving, invest in the following:
Gillette M3 Power razor
King of Shaves shaving gel
Nivea for Men aftershave balm
I usually shave after I've had a shower - the hot water softens up your skin and your facial hair, and makes it easier to shave away. Remember to take your time while shaving. It's not a race, and you won't cut yourself if you take it slowly. Work with the grain as much as you can - running against it will irritate the skin if you do it too much. Keep the water hot and the blades sharp - if you use a three week old razor and mildly warm water, you won't get the best effect. Once you're done, rinse off with cold water and apply a bit of the aftershave balm. I used to have really bad spots, but my skin's awesome these days.