How do I shave my bikini area properly?

Basically, at first I always used to only shave in the direction that the hair was growing, which I know you don't do usually, and which resulted in stubble - but when I tried to shave the opposite way, I got cuts, redness and ingrown hairs galore. I don't know what I'm doing wrong - I looked it up and did everything that people seemed to suggest - shaving gel, new razor head (venus) pulling the skin taught, shaving back the other way to reset the hairs, moisturizing afterwards, but nothing helps! What am I doing wrong?!