Razors have been around for over a 1000 years. Sharp piece of metal. Drag across skin, Exterminate hair. Over the years they have become more "safe" and less likely to slice your skin - but it's still metal and skin!
The big controversy here is if you get goosebumps. You want your skin lubricated so the metal slices across your skin and doesn't burrow into it. But if you get cool somehow and get little goosebumps popping up in your skin, then the razor slices the high point off of those and you bleed.
Also if the hair is limp then the razor just pushes it over instead of cutting it, and the hair isn't trimmed off.
In general, the correct fashion to use with a razor is to first take a warm shower. The spray will fill the hair with water and also puff up your skin with water. That way the hair sticks straight up and is stiff, so it's easy to cut. Put a lotion on your skin so the blade drags smoothly over your skin. If you can put a non-fog mirror in your shower this helps a lot too, if you need to visualize what you're doing.
Use a good, sharp-edged razor. We have found that those 3-blade Mach 3 and Venus razors Actually do a great job for both male and lady shaving. There are new disposable versions of both as well. When your shower is finished, but the room is still warm and steamy, put on a good shaving ointment and shave yourself slowly. Don't rush, you risk a nick.
Some citizens like to shave 'with the grain' because it's more gentle. I find with my thick hair that it leaves stubble when I do this, so I shave 'against the grain' so the blade cuts as low as achievable. You can experiment with both ways on your own body to see which way works best for you.
Aftershave is meant to tighten the skin up and add to your levelness. However if you have ANY nicks it can Undoubtedly hurt. I prefer a creamy solution after a shave, to soften the skin and help any small nicks or scrapes be soothed. Also, lotion helps the hair grow perfectly by keeping the skin soft. That reduces the risk of ingrown hairs (i.e. hairs that don't grow up the hair follicle and instead grow 'into the skin')
It's recommended that you only use a disposable razor around 5 times before replacing it. If you use a blunted razor, you have to press harder to get it to cut the hair, which ends up nicking your skin. It's not worth it.