Shaving's been hell for me ever since the beard creeped down my neck and started growing at all odd angles, and despite all the advice I found online and from friends, I could only conclude that everyone's face is different and so is what may or may not work for you. And yes, I cut myself 50% of the time.
Here's a few things that worked for me, so experiment around with them:
1. Shaving in the shower is the single best approach I've found. It requires a fog-resistant mirror in the shower itself, whether mounted on the wall or through some other fashion. The basic idea is that by the time you're done with all your usual shower stuff, the warm water will have opened your pores and softened your hairs enough to make a shave that much easier. That, and getting all that foam off your face is that much easier for obvious reasons.
2. Everyone else is right that sharp razors are important. It seems the razor companies keep adding an extra blade per razor with every passing year, and I've actually found that more blades means you take fewer strokes to do the same job, and you're that much less likely to bleed. But they don't stay sharp for long, and even worse they can grow bacteria if you use the same one for too long. Thus it's worth the extra money to change frequently.
3. Electric shavers can do a world of good too. The downside is that the ones that are worth anything are pretty damned expensive, but if you find one that works on your face it will make your life so much easier. Still, even with the perfect shaver I eventually found, it does nothing to get the hairs on my neck, so I actually have to combine the two when I shave: first go over it with the electric, then finish the job with the blades.
4. Last word of caution. You look young like you may still be in school, which means you're living in the age of acne. I learned far too late in the game that 90% of my acne simply came from me touching my face with apparently bacteria-contaminated hands - despite the fact that I've always been a compulsive handwasher. And still today, the rare time I get a pimple is usually after a close shave when my face was irritated for one reason or another, and low and behold I touched it excessively. It's something you should do anyway, but this is one more reason to invest in good facial products like an antibacterial face wash (Neutrogina is good) and some moisturizers for when the job's done.
Good luck with your experimentation, and if all else fails, get a dark hand towel and apply pressure until the bleeding stops,
Ben