Waitresses are tricky. As you rightly surmised, they're generally used to being hit on (it's an occupational hazard) and are likely not going to take you seriously. If you're really interested and think she may be too, your best bet is to be straight with her. Just ask her out for drinks and if she wants to she'll arrange it with you.
You've hit on the big issue there. I've said it many a time, confidence is key and it can't be taught. There are two sides to it:
1) You have to believe in yourself. Asking a girl out is like trying to sell a product, only the product you're selling is yourself. Think about all of the positive aspects about yourself that will come across in a first impression sort of scenario. If it helps, actually sit down and make a list and don't worry if it seems stupid. If you think or have been told that you have nice eyes, go with that. If your forearms are particularly attractive, write that one down too. Personally, I have been told many a time that I have nice eyes and beautiful eyelashes, so when I was on the market, I made sure to make eye contact and hold it as much as possible. That's just an example though; I'm sure you can come up with your own. Once you know what you and others like about yourself, you'll feel better; sitting down and enumerating the positive aspects of yourself makes you more aware of them and will take away from any insecurities you may have; this in turn makes it easier to be comfortable in a social setting and approach a girl.
2) You need to realise that rejection is simply a part of dating. There is no man alive that every girl on the planet finds attractive; you're going to get shot down and unless you're built like a greek god you're probably going to get as many girls saying no as you do saying yes. Accept it, know it going in and don't take it personally when it happens. If you get rejected a hundred times it'll be worth it if you find the girl you want to marry (or get laid, whatever your goals are).
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I wake up in the morning more tired than before I slept
I get through cryin' and I'm sadder than before I wept
I get through thinkin' now, and the thoughts have left my head
I get through speakin' and I can't remember, not a word that I said
- Ben Harper, Show Me A Little Shame
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