One thing that really goes far when you make the offer to be a second shooter, is don't plan on being a shooter. Be the gopher, carry stuff, get the coffee, listen, watch, ask questions when the client is not interacting and after the shoot. It's always a smooth transition when you show you are there to learn, not make photos for your portfolio. Wait for the lead photographer to hand you a camera and say "now you have a go at it".
One of the biggest PIA is when someone offers to second shoot and all they are interested in is taking pictures and not learning or earning their way, or getting in the way... I know it seems odd to not pull out a camera, it's just one of those little things that goes a long ways.