There is a button called "Create your own subreddit" on your reddits listing that you can click to create one. You may also find this button in the sidebar of many existing subreddits.
In order to create a subreddit the following criteria must be met:
- Your account must have a minimum amount of positive karma. The exact amount of karma needed is not high, however it is kept secret to prevent spam.
- Your account must be at least 30 days old.
This is to make sure that people spend some time participating on reddit and getting to know how it works, before making a subreddit of their own. It also prevents spammers from using brand-new accounts to create subreddits for their spam.
This is also explained in this thread: "Creating a subreddit"