Here are some basics:
All new users start with a Reputation of 10, and a Rep power of 0. You can gain Rep power by:
1. Longevity. You gain 1 Rep power each year after you join.
2. Activity. You gain 1 Rep power for each 1000 posts.
3. Reputation. You gain 1 Rep power for each 150 Reputation that you have. *This was changed on May 16, 2012. This number used to be 100. So you may notice a decline in your Rep power.
1. Your Rep power can't count until you've written 40 posts. I have reduced this from 100 to make it easier for newcomers to hand out Rep. I think by the 40th post it's safe to assume they're not spammers
2. You won't have your first Rep power until you have 150 Reputation, which you may not have by your 40th post anyway.
1. There is a limit - you can only give up Rep to people 5 times per day. I raised this from 4 on May 16, 2012 to encourage Rep giving (and to make up for increasing the Rep threshold from 100 to 150)
2. You need to give Rep to 10 different people before you go back to the same person. This is to prevent some people from creating two accounts and handing each other Rep over and over again to pad the Rep power.