I'll chime in as a current research technician/research assistant. When I started my job, I had no sense of what mistake was big enough to get me fired. I fretted over everything, drove myself crazy second guessing everything, made tons of dumb mistakes, and was stressed the way you sound stressed. My advice: your mindset should be "what can I learn at work today?" I find it neuroprotective to focus on learning rather than being perfect. That way, even if the only thing you learn on a given day is that you'll never again do what you just did, then you're still coming out ahead.
Other miscellaneous advice:
Others are right: do NOT rely on memorization. Check protocols, walk through protocols before doing the real thing, make to do lists, etc.
Know what your research is about, where it came from, why it's important, and why it's done how it's done. As I was advised on SDN, read the grant proposals. You may not be able to do every procedure perfectly, but you CAN take the initiative to be well-versed in the subject you're researching.
In my lab, we stress that it is ALWAYS better to ask a dumb question for the tenth time than try to do something you're unsure about. Ask people to watch you do something. Take notes watching someone doing something. Ask someone to look at your protocol before you start. And keep your lab notebook up to date.
Be a good employee. Show up on time. Be nice to your coworkers. Be mature. Make it obvious that you want to learn, and try your best. My PI might not find out about or care about every time I make a dumb mistake (assuming I fix it), but she definitely notices that I am good employee who is engaged in the lab's work. Then I get the benefit of the doubt when I do mess up.
Good luck! I have found research to be valuable and rewarding.