The vanilla ice cream will replace half of the milk the box ingredients call for. So just scoop that amount of ice cream and zap it in the microwave for 30 seconds.
You only want it to melt, not heat up, so be cautious not to overdo it. You could also leave the ice cream in the refrigerator for a few hours or overnight to melt it completely.
If you want to experiment with different flavors, try a delicious concoction of banana pudding and chocolate or strawberry ice cream (though it might not be very pretty).