As Worship Pastor in a local church who gets to direct both "traditional" and "contemporary" worship, I have to tackle a great and necessary problem: how do we teach new tunes?
Both styles of worship have their own tools built in to teach new songs, with one style taking a little more prep and time (contemporary) than the other. I've done a lot of research in reading and in practice and I've come up with a roadmap along the way for application in each style of worship.
Teaching in the Contemporary Style
Honestly, teaching a tune properly in this context take a few weeks and discernment along the way.
It starts with getting the congregation to listen to the tune. Just listen. The first time we hear a congregational song is almost always as an offertory. People are accustomed to listening to music during this time anyway as the plate is being passed. It's crucial here though to make sure, if the song is to be taught, that the words have been given to your A/V Team to get on the screens!
The next week, the new song is in the opening set. Opening sets of songs in contemporary worship usually include 3 to 4 songs, so it's pretty safe to include a newer song here. Just make sure it's preceded and followed by a familiar tune! People want to sing, so give them something to sing that they know. We often deal, in established churches, with a melting pot of people. Youth and children grab on to newer tunes quicker than adults (usually), so we need to be sensitive.
I'll then usually skip a week or two and bring the song back. Generally having been heard and experienced three times, I consider a song learned. But where discernment come into play is knowing a song well enough that you, the worship leader, can get off the page and observe the congregation singing. Ask yourself ... Are they singing? Are they engaged? We can't be afraid to say that a song isn't congregational.
I also use online resources to get new tunes out to the congregation ... I'll often include a youtube link to a new song in my weekly staff newsletter and we've just started tweeting the worship setlist the a couple of days before Sunday, with the hope that people will look up the songs.
Teaching in the Traditional Style
I've actually found it easier to teach tunes in this style, but a method is still necessary!
If a new song is to be sung in worship, I always go over it with the choir at the choir practice previous. The choir is a worship leading ensemble, not just there to sing pretty anthems! If they've gotten it down, it'll be that much easier to teach the people.
Then comes Sunday morning. At my current church, we only have the UMH in the pews, so if we're teaching a new tune out of it, I usually have my organist play through the whole tune first. If it's entirely new (new tune and text), I'll instruct the congregation to listen to the choir sing the first stanza, and then jump in on the second. If we're doing a new hymn from TFWS, or Worship and Song, we take this same approach and either have lyrics in the bulletin or on the screens.
I think regardless of what style you're teaching in, prayerful enthusiasm is key to getting the people on board with something new. Don't be afraid! Just as we pray for clean and new hearts on Ash Wednesday, it's important to pray and teach new songs on Sunday morning. Old churches can be new creations!