The shows and live music usually start 6pm or so and continue all evening, here and there. For the big production shows or special guest entertainers they typically do two shows on those nights - an early one and a later one so those with assigned seating dining can get to see it. They don't do the big shows every night. A 7 night cruise will usually have two production shows and the other nights will have lesser shows or perhaps a guest star. On those nights they might only do the show once - again it is usually at a time when everyone with assigned seating might be able to attend. On the nights with only one show my experience is that it is often later - say 10:30 or so.
You can attend either the early or late show, so you'll have to gauge your dinner time accordingly. Show times will be prominently noted in your daily Princess Patter.
I might also add: don't show up just before the show starts and expect to find seats. It is safe to get there 20 minutes or more early so you won't be disappointed. Oftentimes the cruise lines will hold bingo right before the show, and thus the place might be packed with bingo players who then stay put for the show. You'll have to keep an eye on the schedule and see what is planned for the showroom prior to the big performances.