There are a number of sites to upload your songs such as soundcloud or YouTube.
However, once they're uploaded, you're going to need a place to promote them and it's better if it's free.
Here's a method that works well for me.
Start up a Tumblr account and start collecting followers. Once you have a good follower base, post your link to your Tumblr at least 10 times a day.
Also, keep collecting followers you can.
The more followers you have, the bigger chance your song will get shared throughout the community.
This should help you get a kick start to promoting your own songs.