The FAQ mentions access to moderation tools and deletion ability. What are these moderation tools and how can I learn more about them?
Or are they only for people who are actually moderators?
You'll get a tools link; you won't get a mod link. You basically get a bunch of stats -- you can see a list of questions getting close votes, you can see posts by new users, that sort of thing. You can see a list of flags, but you can't do anything special with them that you couldn't already do.
You can vote to delete questions that have been closed for two days. I've been pretty uninclined to delete closed questions personally unless they're spam, but I'm not sure what the Stack Exchange general consensus is on that issue. Oh, and you can vote to undelete deleted questions. I think those two things are the only actual new actions you can take.
It may take a day for them to show up, but I think a "mod" menu will appear up top for you. It's mainly self explanatory. Read A Theory of Moderation.
Also, here's the tips I got emailed by Robert Cartiano when I became a mod:
Tip 1: When you vote to close or delete, your "vote" is binding (i.e. it happens immediately). So your "vote" is no longer part of the democratic process. You've got the "super vote!" As a general rule, I try not to apply Moderator function to activities that are being addressed by the community. If a post looks like a duplicate, you might give the community the chance to take care of it. If the community won't (or can't) act, do your thing. You have a bit more leeway early on because few people have the reputation to close. And certainly take immediate action on blatant problems (obvious spam, illegal activities, language, etc).
Tip 2: Flagging: Users flag things for all sorts of crazy reasons. You will act on a pretty small percentage of them. Users will flag saying "this is a dupe" and "this is subjective" and, my favorite, "This is spam." Users call anything they don't like "spam," trying to get rid of posts through you as a super-vote-by-proxy. Remember, there is a community voting on this stuff. You don't have to act on everything when the community can decide for themselves.
In general, I'll delete the flag when I act on it (or the community acts on it [closed]). If I don't act on the flag, I will leave it there for reference. When the list starts getting long, I will start deleting old flags after some time has passed.
Tip 3: Leave breadcrumbs: Ideally, the community should police itself. But sometimes you have to act and you should try to take the opportunity to let members know what you did. Leave a comment saying things like "It's better if we don't split the answers up between multiple threads so I am closing this as a duplicate." New users will see these signposts and learn to use the system that much quicker.