In the latest Stack Overflow election, the minimum requirements were (emphasis mine):
In the nomination phase, any community member in good standing with more than 3,000 reputation may nominate themselves to be a community moderator.
For the Stack Overflow election, an eligible candidate for the election must have all of the following badges:
In the other sites of the network, the reputation requirement is 300, and there are no badge requirements, check out the latest Super User election page for example. On Beta sites there are no elections, moderators are appointed directly by Stack Exchange.
These requirements are subject to change at any time at Stack Exchange's discretion. Another requirement that is not immediately obvious is that you will have to abide by the Moderator Agreement. Even if elected, Stack Exchange may remove your diamond at any time if you don't follow the agreement's terms.
Your meta participation and helpful flags are also very important. Take a look at Yi Jiang's Moderator Candidate Statistics, to get a better feeling of what people usually look for in a moderator. To better understand what a moderator's role is, you should also read: