Performing in character
Your route into a character or song can come from many different sources - there's no one right way. Imagine, for example, playing Little Red Riding Hood's wolfish stalker in the musical Into the Woods. For inspiration, some actors would take a trip to the zoo, to find out how wolves behave. Others, who work from external factors, would need to find the very shoes or clothes that make the character real - the top hat, perhaps. Others like to work from the text itself, taking not only what the character says, but what others say about them, and deciding which parts speak truly. Of course, the music itself also tells you a huge amount about the character and the emotional path of the story.
When singing in musicals, you have to perform in a heightened manner in order to be able to launch from speech into song. You can't speak at your normal level and then jump into song and expect it to be credible. In rehearsal, try muttering to yourself before your lines come up, so as to build up your energy levels before it's time to speak. Then speak with more energy as you come up to a song. You'll probably be speaking over a musical introduction, which will demand this energy anyway.