Generally, peds applications do not "require" away rotations like some other specialties. The only real reason to do one for peds would be if you were very interested in a particular program/location. That being said, doing an away rotation is a double-edged sword---be aware.
But to answer your question, obtaining away rotations involve the VSLO/VSAS process. Each program will have its own requirements. Generally, obtaining away rotations is a combination of submitting timely and well-written applications with your CV playing an important part as well. Some may involve LORs and personal statements which are very important too.
For peds, I'll bet you all the donuts in Dunkin' that obtaining an away will come down to submitting on time and *maybe* your application. Literally almost no one does peds aways, so I think you should be fine. I have a feeling that it's a "anyone who wants an away will get one" in peds because of this. Someone else please correct me if I'm wrong.
Specialty dependent but usually not hard. It's usually first come first serve. If you're in competitive specialties, may be harder to get a time block that you want, but not hard generally to get an away at the place you want. You're pretty much very low cost for the schools as you're responsible for living and board there, so they don't really care.