Nice video from CoinWeek with a live NGC coin submission at a show.
Generally you should only use PCGS or NGC or maybe ANACS, but probably not ANACS without reason. Anyone else adds no value.
Me, I like NGC as they are the cheaper of the big two.
NGC is the leader in ancient coin certification too and that is something I collect myself.
Now many ancient collectors prefer their coins raw, myself included. That being said if I buy one slabbed, I keep it slabbed as I know it will aid in the resale value and speed come time to sell.
Anyway, check out the video for a look at the grading process.