Conduct a search for "Internet radio" using your favorite search engine. There are many Internet radio networks and stations available for you to choose from.
Explore the different stations and options available. Some Internet radio networks divide their stations according to genre and some allow you to create your own station based on your musical preferences. Choosing a network that allows you to create your own station will allow you to listen to a very specific sub-genre of music, such as melancholy music.
Enter the titles of melancholy songs or artists whose work you enjoy. If you need a place to start, Damien Rice, Ben Harper, Conor Oberst and Coldplay are all artists who frequently release melancholy music. Ask friends for recommendations of melancholy music they enjoy.
Rank the songs that the radio station plays if you are given the option. By ranking the music you will help guide the station to play music according to your tastes.