You can read all about how to create a community in our Mod Help Center. There are two criteria needed for a reddit account to be able to create a subreddit:
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 community of their own. It also prevents spammers from using brand-new accounts to create communities for their spam.
Existing subreddits that have been abandoned or where the current moderators are inactive may be requested via r/redditrequest.