Record a demo. Put your best songs on there first. Most record labels will only listening to the beginning parts of a CD since they go through so many. Also, find out who you need to send the record to. If you send your demo in the attention of a particular person, it will most likely get heard than if you just sent it to the company's address and end up in a huge heap of other demos.
Research on how to make your demo better. There are loads of books and websites that offer helpful tips to making a better demo (see Resources below).
Attend local shows. There are often contests that offer money and even recording time for the winners. Sometimes talent scouts check out these shows and you may give them the show that they're looking for.
Practice your talent anywhere and everywhere. You never know when you are going to be in the right place at the right time. If you're around a lot of people at the bus stop or school, start laying down a line or two. If the right person hears you, you may end up with a record deal.
Make a name for yourself. Create your own website or MySpace page to create a buzz about your music. Add snippets of your songs and places where you're performing. A large crowd will draw attention and if you create a hype about yourself, you'll find yourself in demand and signing a contract in no time.