Think about why you want to cruise, and what your priorities are. Whether it may be comfort, good food, activities, ship size, or your budget, you and your travel agent will be able to pick the perfect cruise line for you, if you both know what your expectations are first hand. Having realistic expectations of what a cruise is all about, and understanding what your cruise is, and what is not, will ensure that you have a great time on your first cruising experience.
Do your research. This will be easy for an obsessive person, less so for someone more spontaneous, but it pays off on the cruise itself. Understanding the logistics of your cruise - getting to the port, embarkation, luggage tags and the like, and taking the time to plan your cruise is well worth to ensure you will have a smooth, worry free vacation.
Join online cruise sites and discussion boards, and talk to others about their experiences. Ask questions, the people on these boards are usually experienced cruisers who like to help. You can even meet some folks on these online boards before cruising, and then met up on the ship.
Get to know your ship. Spend some time looking at the ship layouts, so that you have an idea of what's available onboard and were to find it. Yes, you can find all this out when you get on board, but you'll want to spend more time on board enjoying yourself, not working out where the buffet or where the gym are located. Ask your travel agent about your options for shore excursions. Most ports of call are set up for cruise visitors, so finding your way around isn't hard.
Pack light - okay, everyone says this, but you don't need that much gear on a ship, unless you want to really dress up for the formal dinner nights. It is also a good idea to take a carry-on with essential gear in case your suitcases don't turn up in your cabin quickly, sometimes bags can arrive a few hours later.
Don't stress about getting sea-sick as the ride on modern ocean cruise ships is stabilized and incredibly smooth, and river cruise ships have always been very stabile (with the exception of the mouths of the great rivers). - although it is never a bad idea to take medication with you just in case.