Above and beyond all else, do what your comfortable with.
My last girlfriend turned me on to eating out her ass. I was very hesitant at first but it soon turned into a huge turn on for me.
I would start with running my tongue in circles around her hole to moisten things up. Remember, the ass isn't self lubricating, so going too rough at first might be....well....too rough. Then try flicking your tongue in one concentrated area, maybe right on her hole, maybe at 12 0'clock or 6. You can try 'tongue fucking' too if you get comfortable. If you enoy it, then just lap away, get her wet, get her soaked, guide her to play with her clit at the same time.
Rule o' thumb. (the women will back me up here, i'm sure) EVERY girl is different. They all like it differently, so just pay attention to what really gets her going and go with it! Obviously she's into it for a reason, so odds are if you put some effort into it and enjoy it yourself. She'll be begging for more!

If your worried about cleanliness, try starting by showering with her and taking special care to wash her asshole for her ;) could be fun for both of you.