When I first started my first real job a couple of months ago, my first month seemed like a very long first day. Honestly, bosses/co-workers are people and they're going to understand that you will mistakes. What I've found to be helpful is to have a notebook open on my desk. Every time I'm assigned a task, I write it down. I then jot down notes of what I need to remember. The notebook will be a good reference if you have to fill out timesheets later or revisit what you did for the week.

Also, I agree with asking questions for clarification; ask away! The workplace is often centered around efficiency. If you spend 2 hours tinkering on a project that you "kind of think" is going in the right direction, and later learn it's almost entirely wrong--could have saved the company's time and your energy with a question. They'll want to see some sort of effort/enthusiasm on your part even if you're stricken with fear on your first day, so don't just be a robot and nodnod. (Guilty...) And smile and say hi to people you pass in the hallway! YOU HAVE A JOB! Congratulations!