The current Hunters in the roster are:
Ah Muzen Cab
Anhur
Apollo
Artemis
Cupid
Hou Yi
Medusa
Neith
Rama
Ullr
Xbalanque
Keep an eye out for which ones pop up in the free rotation.
To master a god you need to earn 50 Worshipers while playing as that god.
The following is taken straight from
http://smite.gamepedia.com/Game_Elements#God_Masteries_.26_W...Conquest you earn .25 of a worshipper per minute played and winning a match gets you 5 more on top of what was earned in the match.
All other versus modes (Joust/Arena/Assault/Siege) you get .2 of a worshipper per minute played and winning a match gets you an additional 4 worshippers.
If you are just getting used to Smite and have done the tutorials I would recommend going into Arena matches. Currently my arena matches last around 15 minutes. With a win that's 8 worshippers per match. So that's 7 Wins or 13 losses to reach God Mastery Rank 1. Conquest games run longer so you need to determine if you want a couple arena matches to every one conquest.
I would recommend playing regularly, getting used to the game and finding out what gods you like and don't like. This will get you a good stable of gods to select from and get you quite a few that hit Mastery Rank 1. You can get to Rank 1 using auto buy skills and items in a couple hours.
Boosters which you can buy in the marketplace give you a 25% increase to worshippers earned. Though these costs gems which are purchased with real money.
Lastly, keep an eye out for double worshipper weekends as this will cut the amount of matches required in half!
Let me know if I missed anything or if you have any questions.