Before I start to explain things, I'll point you to Reddit Enhancement Suite, which expands on reddit, letting you organize your subscribed, tag other users, save posts and comments, etc. I also use Hoverzoom so I don't have to click everything.
Reddit's like a giant forum, of which you can choose which subforums (called subreddits) you want to subscribe. To subscribe to a subreddit you visit its page and click the subscribe button on the right. Popular posts from your subscribed subreddits will appear on the front page.
Here's a warning though: There's a subreddit for just about everything, with some of them pushing the edge of legality. There's some fucked up stuff on reddit, so be very careful about what you click.