Something that we do quite often when learning a new song for our worship repertoire is first getting a copy of the new song in audio format (mp3, CD, etc) to the instrumentalists and vocalists on the worship teams. Then they have the chance to be prepared to play the song including specific beats/rhythms, riffs, runs, etc.
We also many times will introduce the song to the congregation in the same way that it is played on the CD including those beats, riffs, runs and such. We try to do the song very closely to what it sounds like on recording (at least for the first time) rather than putting our own spin on it. Then after we’ve taught it one or two times to our congregation we can start putting our own arrangements together for it.
I find that doing this helps our musicians and vocalists grow by giving them more techniques to use in their own toolbox, helps them to be in sync with the team and learn what that feels like, and helps us as a team learn how to arrange the whole (rather than them seeing only their part).
One additional thing we do with new songs is playing them two weeks in a row or twice in the same month at the least. The first time someone hears something they are learning, by the second time you do the song- they can start worshipping with it because its starting to become familiar.
Its not rocket science, but it works. What do your teams do to introduce new songs?