First, are you doing a hot water soak? Give your hair 3-5 minutes under comfortably hot water, it opens and softens the follicles, making them easier to cut through.

Secondly, find a shaving cream that works for your skin. I use a cheap sensitive skin kind with aloe and oatmeal, this keeps the skin soft and minimizes irritation(the bumpiness).

Two passes with the razor, one with the hairs growth direction, the other against. Be very light, you should just feel the razor head against your skin. Pressure leads to skin getting caught, and that leads to cuts. If you feel like you need pressure to cut, your blades are too dull.

Keep the skin taut by doing things like opening your mouth, or pulling on your skin lightly. Taut skin is smooth skin, less risk of cutting yourself.

For any irritation after, find a light lotion. You don’t want something too heavy or greasy, just a gentle moisturizer. A part of irritation is from the skin getting dry alongside the abrasions.

EDIT: If using a disposable/replaceable head, try different blade counts. Some people do great with 1-2 blade heads, some have a better response with 3-5 blade heads. That really comes down to your skin and hair. It’s a trial, but once you work out which is best, it’s consistent regardless of brand.

I’d you’re doing legs, arms, or genitals, a contouring razor is your best friend, it flexes along your curves better than other razors designed for the face/throat.