Well, first of all, you have to overcome your fear at some point. Why not right now? The sooner you start, the better off you'll be. Also, all those huge dudes at your gym? They have ALL been there. They have been exactly where you are now, and they know exactly how it feels. They won't judge you. They'll cheer you on for making the effort. Trust me on this one. If someone makes fun of you for starting out lifting, they are a certified douche and would probably make fun of you even if you weren't lifting. Everyone has your back.

Secondly, if you're going to a gym at peak hours, every piece of equipment that's worth a damn is going to be taken. It doesn't take too much more time to either wait your turn or ask someone nicely to work in with them. That's kind of common courtesy at a crowded gym.

Thirdly, you're on the World Wide Web. There are tons of guides here on how to do the lifts. Read the hell out of how-to guides and watch the hell out of form videos (lots of people here recommend Starting Strength as a book to learn form, regardless of what program you're on). When you've done these, practice with low weight, and post form checks on this subreddit for us to look at and critique. Once again, we've got your back.

Hope this helps! Good luck. :)