Clarify the nature of the event. There is a "religious service exemption" in the copyright law, which allows church choirs and soloists to perform copyrighted music during a service without prior permission or subsequent penalty. This exemption does not cover concerts. You can perform a copyrighted piece during a Sunday evening church service, but not during a Sunday evening concert or a Sunday afternoon music program at a local nursing home, except with permission.
Find the copyright holder. To get permission to play an artist's pre-recorded music, copy sheet music for an accompanist, print lyrics of copyrighted songs in a bulletin or make audio or video recordings of your service, you must contact the copyright holder of the music and obtain permission. Every piece of printed music and all CDs will have a copyright notice printed on it, consisting of the copyright symbol (c) for printed or (p) for audio, the date of the copyright, and the identity of the copyright holder.
Obtain permission. If you have time, write the copyright holder, explain how and when you wish to use their material, and request written permission to use it. Include a self-addressed, stamped envelope for their convenience in reply. If you don't have time, many music publishing companies are able to give permission over the phone with a follow-up written permission. You must follow all requirements of the copyright owner, including payment, in order to legally use the music as requested.