First, it can be helpful to find out which Publisher owns the song's composition and which Performance Rights Organization (PRO) manages the licensing for the exact arrangement you are looking for. To do that, you can search each PRO's online catalog (repertory):
Second, if you are not part of an organization which already has a "blanket license" with the PRO which manages the song you are looking to use, you can contact the individual PRO for permission to perform the song. Each PRO is different, but typically, you can expect to wait -----, to pay -----
One of the easiest ways for ministries to navigate performing copyrighted music at ministry events that fall outside of the Religious Service Exemption is by securing a license especially designed for churches like the one from Christian Copyright Solutions.