I read a post this morning at The Worship Community and it had some very good advice on introducing original songs to your praise team. I don’t know how many churches sing songs that are generated out of their praise team or out of their own worship times, but I would encourage you, as a worship leader or praise team member, to begin looking for music that is coming up out of your church. My church, CWOC, has a few songs that are original to us and they are some of the most powerful songs that we can sing. There is something to be said about being able to look at the name at the bottom of the song and realize the writer is standing there beside you.
The reason is because, when a song is an original to your church, you are able to not only hear the heart of the one writing it, but you can also see it. The article, Tips for Introducing Original Songs, gives some excellent advice on how to begin using songs that are coming out of your church. It not only gives advice on how to introduce the song itself, but also how to tweak it and allow the song to become everything God wants it to be.
Read the article, and then begin cultivating an atmosphere where the musicians at your church are encouraged to share their heart through lyrics and music.