To master a god you need to earn 1000 Worshipers while playing as that god.
The following is taken straight from
http://smite.gamepedia.com/Game_Elements#God_Masteries_.26_W...As dontVanek says the differences have been patched out so pick your favourite mode.
A bit of math as currently my arena matches last around 15 minutes. With a win that's 8 worshippers per match. So that's 125 Wins or 250 losses to reach God Mastery Rank 10. Conquest games run longer so you need to determine if you want a couple arena matches to every one conquest.
If you've been trying for the other Master achievements you should know which class is your favourite and which god you love the most. Or you will grow to love them as you will be at this for a while.
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.