Create a set or collection of songs you have written that you are happy and confident about playing and distributing. It is easier to not have to worry or think about whether they sound any good while you are peddling your wares. Focusing on the act of getting your songs heard is the best thing you can do.
Upload copies of your songs to the web so that they are available either to buy or download, or simply just available to be heard. There are thousands of sites on the web that can accommodate a musical profile page for your band or act. Myspace and Soundcloud are popular choices.
Approach your local radio station to find out if it has a show or radio slot that champions unheard music. This is a great way to get your songs heard by a great many people. Forge a good relationship with a DJ so future airings of your songs are more likely as you become better known.
Busk. There is nothing more direct than playing your songs on the street. It can be a difficult experience, but you can be sure that your songs are definitely being heard. You never know, if you are good enough to create a crowd from the busy people in the street, your songs might actually have the potential to be very popular.
Do gigs and concerts anywhere you can. Any venue that has facilities for you to play your songs is a venue you should embrace. Open-mic nights usually are popular and regular gigs that you can try out your songs without having to go to the trouble of organizing a concert.
Drop some Compact Disks (CDs) into some local bars and clubs to see if they will add your songs to their play lists. It can be a good barometer of your work if it can stand up in a live commercial environment, albeit playing in the background while people are enjoying themselves.