Yes, wear a condom and use plenty of lubrication. The condom will protect both of you against any stds.

Yes it's safe. I'd suggest a non-latex condom, they're a lot easier on rectal walls. Lots of lube, lots of lots of foreplay to get her ready.

Isn't it dirty? does the girl need to do any prep?

Yep, it's dirty. You're using a hole used for waste removal. It's one of the good reasons to use a condom. Have a damp towel nearby for cleanup.
It's a good idea if you can convince her to practice either with a toy or her fingers. It will allow her to better control her rectal muscles during penetration.