In discussing transitions, we're assuming you've come up with multiple-tune medleys. A nice medley is a definite way to sound like a real band. One reason for this is that a transition from one tune to the next is a stellar moment - it takes a dance and a mood that's been internalized by the dancers and shifts it to a new level. This can be done in many ways. Sometimes just moving subtly into the next tune has its own excitement, but more often it sounds better to set the new tune apart somehow.
Transitions can resemble endings, by using the methods of cutting the tune off or building volume.
Find chord progressions that link the tunes. Sometimes we change the last bit of melody to make a nicer connection. There are a few rhythmic variations that are typical in arranging dance tunes. Be extremely careful with this last one - remember, you have to keep solid rhythm going at all times. We've also borrowed lots of rhythmic ideas from other kinds of dance music, e.g. calypso, swing, ragtime, etc.