If you've never been on a cruise before, the idea can be pretty scary. All alone in the sea with no way out can inspire nightmares among the uninitiated. The first advice to give to someone who has never sailed before is that they understand that a cruise ship is like a big city. There will always be plenty to do and lots of people around, so you don't have to feel isolated or alone. And the cruises have learned from the error of the Titanic and other films about the fear of the sea. They all have lots of lifeboats and safety instructions, so you'll be given a lot of notice if the unthinkable happens.
In your city you will generally gravitate towards what you know, and it will be the same on a cruise ship. However, don't limit yourself to what you know; be adventurous and try new things. Many cruises offer dance lessons, be brave and sign up. Some will also have karaoke nights, so show your voice to the world, or at least the small section that they are on a cruise. You will not know these things unless you look at them, so take a detailed itinerary of the ship before you leave and take note of everything that sounds interesting.
You will also pay a long walk around the ship as soon as you get in so you can get an idea of where everything is, as well as find the best way to reach the dining room for dinner.