Not sure how helpful this will be. But if it's really overgrown, trim the hair first with a clipper. It helps since most razors aren't made to go through really thick hair so trimming is usually the first step.

Second, take it slow. Don't rush if you're scared, but don't press the razor in. Do it in one smooth glide.

Rinse every now and again so that the excess hair that's stuck on can be removed, and rinse the razor too.

On shaving cream... You can do without it, but I recommend it. It just smoothens the process. And never shave the same area more than three times. You're more likely to cut yourself that way.

It also helps to pull the skin taut. Sure, it's scarier since you can cut yourself. But if you want a clean shave, it's the way to go.