how to root your phone?(android)

there are lots of tool to root mobile phone,Framaroot/towelroot/kingroot etc.,
u can google for it ,here is the tutorials collected from internet

note:there is risk on your phone security


Root via PC
http://www.droidviews.com/rooting-guides/
http://howtorootmobile.com/how-to-root/

Root via mobile phone
http://theunlockr.com/2013/11/30/root-android-device-framaroot-method/
https://www.youtube.com/watch?v=HMbVtKjWvJA

Could you list some benefits of rooting a droid? I'm about to buy a Galaxy probs. I know it let's you run certain apps like screenshot and apparently it's for cuztomization but I don't know much besides it voids your warranty.