It is usual to have 'casual', 'smart casual' and 'formal' nights. Working backwards, 'Formal' is dinner jacket or suit for men, 'Smart casual' usually means with a sports jacket (but not so much nowadays) and 'casual' is open shirt, but no jeans & trainers or shorts. I'm sure you can work out ladies dress from that. Sounds like you are doing about a 7 day cruise. In that case you will probably have 1 formal, 2 smart casuals and 4 casual. If its a 14 night, 3 formal, 4 or 5 S. Casual and 6 or 7 casual. For more info than you can shake a stick at, go to www.cruisecritic.com
Join the roll call for your ship and 'talk' to your fellow passengers before boarding.