As you already know, you start on the 1st tee and what you do is tee up your ball on a small tee (the wooden 2 1/8 inch variety are best) behind the two markers you will see - do not tee your ball up in front of them because that is against the rules.
Usually you will toss a coin to see who in your group starts off first. You aim down the fairway towards the green your playing, in this case, hole #1. The person with the lowest score on each hole has the "honor" and tees off first on the following hole. You always tee off in the order of the score you got on the previous hole - the low scores go first.
So, if John got a 3, Sally got a 4, Sam got an 8 and Sandy got a 5 on hole #1 - what is the order of teeing off (hitting from the teeing ground) on the second hole?
The order would be John first, then Sally, Sandy and then Sam.
So, what the quickest way to learn how to play golf?
The quickest way would be to just go out and play with your friends, preferably some who have been playing for a while. Starting out on a par 3 course would also be easier because the holes are shorter. You could also take some lessons in person with a local golf pro - look in the yellow pages or just go to or phone a driving range or golf club and ask if they give lessons. Be sure the lessons are from a certified PGA, LPGA or CPGA (Canada) golf professional. Or, use the shortcut beow.
Also, watch some videos, or read some books, on how to start out in golf.