Play to your specific audience. If your songs are in the rock genre, find gigs at rock clubs with open-mic nights for up-and-coming artists. The more buzz you can build among your particular fan base, the more likely it is that you will be noticed by an industry insider.
Build a strong street team. To get fans to come to your live shows and purchase your CDs, you need a strong street team. These are the people who will do the groundwork for you: talking to potential fans, selling CDs when possible and distributing promotional material about you and your music. Find local college students, if possible, since they are often willing to volunteer for a street team in exchange for free CDs or T-shirts. This provides you with street team coverage without having to pay out of pocket for it. You might also solicit fans of your music to work on your street team; if they are supporters of your music, they may be willing to help spread the word about it.
Submit copies of your song to your local radio station. The station may only play your music during a local's only showcase, but the point is to catch the attention of the DJ. If he likes it, he may provide an in to the station's program director for regular rotation. Don't take a blanket approach here. Only submit your songs to stations that play the kind of music you make. Keep in mind that commercial radio stations are tough for local artists. You might try to get your music played on a college or independent radio station, which may be more supportive of local musicians.
Offer to play local events and festivals. As a musician, the single best way to get your songs noticed is to make sure people hear them. Offer to play a free concert at a local event or community gathering. Set up a table near the stage to sell CDs and pass out promotional materials. The more exposure you get, the more your music gets noticed.
Join a local songwriter's association. Not only are these groups good for support as you launch your music career, but they provide networking opportunities with other musicians, who may have contacts you don't. If there isn't one in your city, contact the group geographically closest to you or find one online that you can join.