Study barbershop music through downloads, CDs and DVDs to trigger ideas, especially in terms of how the harmonies are arranged within the structure of the song. You will need to remember that a traditional barbershop quartet is comprised of a lead singer, who will sing the melody, plus a tenor, bass and baritone who will harmonize around it.
Compose your song, always being conscious of how it will work in a barbershop context. Don't fall into the trap of trying to write a traditional pop song. This may work when arranged for a barbershop group, but it won't always be the case. The song should be light, musically. Lyrically, there are no restrictions, as it is really the singing which should be at the forefront of the composer's mind.
Make a demo recording of your song, with one vocal, accompanied by a piano or keyboard. Though the voice here can be at the same pitch on the demo, it will enable you to envisage how the four vocal parts will work together on the song.
Go over the song with a barbershop quartet. This will be the main indicator as to whether anything needs changing. It will be the first time that you will get to hear your song sung in a barbershop style, so it'll allow you to hear if all the vocal parts are in order.