You begin by learning how to get the most out of your camera equipment so your images will look good under all types of lighting conditions. Then, you begin shooting all types of sports so you can hone your skills. You take your very best images to create a portfolio and weed out your least best with better images as time goes by. Once you have a fantastic portfolio and you have proven to yourself that you can get brilliant shots on a consistant basis, you start presenting your portfolio to various media outlets if they will allow you the opportunity. There are tons of photographers who aspire to shoot professional sports, so the competition is unbelievably tough, you'll need plenty of luck along with stunning portfolio to get chance at shooting pro sports. In the end, if you finally get to shoot pro sports, you'll have to assess if it pays enough to support your lifestyle.
Frank has got it spot on. . I found that consistancey was the key. . dark..poor lighting...raining. . It doesnt matter to them. . They want and demand good high quality images all the time. . not excusses. . You cant have "a bad day". . If you do have one of those days there are another 20-30 people ready to take your place. .
Get yourself some business cards, whilst you are at a game or track meeting or what ever you shoot, hand them out. . If you are good you will get noticed. (Though there is a bit of luck involved as well, being in the right place at the right time to get that one shots that no one else has. . )
It's taken me about 18-24 months to get this far and lots of hard work. .
A typical Superbike meeting starts on a Thursday night. . Checking equipment, making sure everything is ok. . Early start on Friday morning, normally between 0430-0600hrs depending on what part of the country (I'm in the UK).
Once at the track, meet the teams for a chat about what they would like/require. etc etc. Shoot from (normally) 0900hrs -1800hrs, then sort through the good and bad shots, (2-3k of images) get them processed and uploaded to the various mags/papers. . Usually get to sleep about 0000-0100hrs then repeat for the next 2 days. .
Pay's not that good either. .and have to fit all this in around my day job. .
It's not as glamourous as the pics make it look, but I'm having a great time doing it. . .and would'nt change it for the world. . .
I shoot some college and minor league stuff as well as some pro volleyball. As Darren and Jason have said, hard work plus gear. I just kept submitting stuff to magazines before a few called me back asking for the hi-res files for publication. Then it was can you shoot this and that for us. I was ecstatic when NCAA Photos asked me to shoot the women's lax finals this year. I was more ecstatic that they agreed to pay me my day rate for a single game plus travel expenses and royalties. The day rate sounded great until I figured that I had to be there 2 hours before the game, it was a 2 hour game, I had to stay 2 hours after the game then had to upload my top 25 based on the list of shots they needed 2 hours later or no later than 4 hours after the end of the game. Oh and the photos had to be fully captioned per their 7-pages of instructions.
Also, I would suggest you get the gear you need as Darren suggested. There is a minimum you need and you can't say I will get this if I get this work. Just get it. For field sports a D3 and either a 400/2.8 or a 600/4 would be a minimum.
Sometimes you just get lucky. A friend of mine got a call from Michael Strahan. After my buddy finished taking portraits of Strahan's dogs they got to talking and now my buddy has season credentials to the Giants games every year since then. That was years ago, but he did get invited to shoot the Super Bowl from the sidelines.