My musical schooling taught me a lot about music theory and song structure. Everything I studied and practiced was in nice, logical, symmetrical phrases -- four bars, eight bars, 12 bars -- until it was totally ingrained in my playing. So when I found myself in a situation that had a large contingent of unschooled performers, my training wasn't always helpful. There are musicians who don't appreciate that phrases are ?supposed to be? four bars long. These people are inclined to think that a line is a line, and once it's sung it's time to move on. Hmmm. The result is something I like to call 11 1/2 bar blues.
I learned the hard way that sitting at the back of the bandstand and expecting -- even insisting on -- 'correct' doesn't fly. Untrained musicians are sometimes not skillful enough to pick up on any irregularities and make an adjustment. So it's up to the rest of the band to cope. As a professional, I sought to work out these occasional wrinkles so they would come across as seamless. All it takes is a bit of thought and mechanical work.
First of all, start listening and counting. What is the basic structure of the tune? Most of it will be logical phrases. Then watch for the oddities -- usually an extra half bar or a dropped half bar at the end of a phrase. And despite this little bit of creative license, singers/songwriters rarely go out of time by adding or dropping a single beat (but watch out for the occasional bar of 3).
Now, where does that odd bar occur? Likely it's consistent: the end of the phrase leading into the chorus, for example. Once you're aware of the adjustment, all you need to do is remember it's there and play it as if it's a normal part of the tune ... which it is.
This is not meant as a criticism of musicians who weren?t ruthlessly schooled in traditional phrasing. I played with a songwriter who threw in all sorts of creative phrasing. It took some effort, but I managed to cope. It wasn't until I had a chance to sit in the audience and listen to these same tunes that I was able to hear that the phrases were perfectly logical given the nature of the song's lyrics.
And really that's all there is to it. It comes down to learning the tune, no matter how unusual the phrasing and structure might be. And if there's no chance to rehearse and learn the tunes beforehand, let your ears be your guide. And remember to count.