Looks like for starters, you can use gingerbreak; or unrevoked
[How-to] Root your Play - xda-developers
http://forum.xda-developers.com/showthread.php?t=788776
Pros, you get superuser access to the super top secret area of android carriers don;t want you to know about.
Why? well for starters, it takes revenue away from them (most importantly). Secondly, if you don't know what you're doing, you'll fubar your device and give then support headaches.
1. Know your device. Know how to make a recovery backup before you ever begin. And I'm not talking about the app in your device, because if it goes to bootloop hell, your carrier app is useless. Know how to boot to Recovery. Most devices have this, it's a combination of (device off) holding power and vol +. Note that some devices may not have this, until you root and a recovery is installed. Some devices have a combo of 3 buttons.
2. Always make recovery backups. Before and after each process completes.
3, Follow the instructions explicitly. If they require you to check a version of something, there is a damn good reason for it. Do not ever think, you are smarter than the person who made the steps. No matter how odd they may seem.
4. Alcohol. To muster up the nerve.
rooting should be fairly simple in your case. Follow the steps.
when it comes to flashing a new rom, repeat the above
They say it voids your warranty, only because they want to cheat you out of money. But really, when you turn a device in for service, they connect it to a "black box" that flashes everything regardless of what you did to it.
It sounds bad, and you will see lots of red warnings, but really, it's only because they don't want you crying to them if something happens.
Typically, rooting is 95% successful, more if you follow instructions.
Get the alcohol