Alternative music is a musical genre that began emerging in the 1980s and became popular in the 1990s. While the alternative genre takes it lead from the punk movement in the 1970s, alternative has evolved to take on a more melodic approach musically and a less political and social approach lyrically. A great deal of the alternative music in the 1990s incorporated mainstream elements, going against the original stance of the genre. Today alternative music is more easily identified by the way it's marketed than by the songwriting itself. Alternative music is still alive in the twenty-first century, in spite of, or because of, mainstream acceptance of the genre.
Write lyrics for your song. Some composers might start with a chord progression or a particular musical part for the song. You can do this as well, but if you can start with a lyric approach, it may help construct the song. Alternative lyrics used to be extremely social. While social and political lyrics are still used in some alternative songs today, bands like the Goo Goo Dolls, 3 Doors Down and Matchbox 20 have helped bring alternative lyrics more into the mainstream, opening the door for alternative song composers to write lyrics on just about any topic. "Black Balloon" by the Goo Goo Dolls is about a girl with a heroin addiction.
Work out the chord progression for your song. Bands classified as alternative such as the Goo Goo Dolls, Matchbox 20, Foo Fighters and Counting Crows write a lot of songs that work well on acoustic guitar, so use an acoustic guitar to build the song if possible. Sing the lyrics as you strum different chords. Write the chords in over the lyrics when you find the chords you're looking for. Work the basic structure of your song (verse, chorus and bridge) up this way.
Develop the song from the basic structure. How you do this depends on your personal writing habits. A lot of alternative bands have a primary songwriter, but this is only a guideline, not a set rule. You might take your basic lead sheet to your band and allow the individual members to come up with specific musical lines based upon your lead sheet. You might write the parts out fully yourself, including guitar solo, bass part and maybe even the drum.
Record a rough demo of your song to take to the band to go along with a lead sheet. Work through the song with the band to see how your song works. You may write new lyrics during the song rehearsal section. You might find parts of the song you want to drop. The tempo and arrangement of the song might change at this point. With your band is where the song is truly born and comes to life.