There are two primary ways a short story writer can get their name and stories out there in the world: a contest or an anthology. It's not easy breaking into the writing world and even if you have a book written, you're going to need a little street cred before sending it to an agent.
Anthologies are a great way to earn that street cred. Most of the time an anthology is written around a specific topic and you must write a story that fits with that topic. You then send it in and if it is accepted, then you not only get paid for it, but also get published. You may also get royalty payments from the sale of the book.
There are many anthologies out there every year from big and small publishing companies. They allow you to start getting a fan base and the more you get published, the more fans you get. Your fan base is always a consideration when agents look at your work.
Contests are much more loose and may not have a specific topic. Generally, there is an entry fee for each manuscript you enter with most of it going to pay the winner. In some of the larger contests, you can win thousands of dollars and have it published in a special anthology or in the magazine.
These are great because you can win money and earn respect. Some of these contests are major and can catapult you into cross hairs of agents and publishing companies.