If you don't know much about cruising, be sure to get a specialist. There are little tips and things you should know about each ship and line that are very important. Carnival is going to be the least expensive line, but the quality is no where near that of other lines. You are going to see more drinking, gambling, smoking, partying, etc that other ships. Royal Caribbean is a little more costly, but definately worth the upgrade.
You will have lots of ports to choose from with your cruise. So the best way to save money is see which home port, the port the ship leaves from, is the cheapest for you to fly into.
But again, be sure to find a travel agent that specilizes in cruises. They will help you plan an amazing trip and get everything you want out of it and also be able to provide you with advice and tips. Also, my travel agent often has group rates available for me when I go. It can save you more money if your agent offers these.
A lot of people say the best thing to do is book with sites like Expeida, Orbitz, etc. I don't agree at all. The reason is that so many people have had problems booking with these sites. The main thing is that they are not travel agents and will not help you with your trip. If there is a problem, many times they will not help you with it. Not to mention that many cruise lines do not work with bookings that were booked with these sites. I just read a story a few days ago where a lady booked her trip with Cosco because they were giving her $200, so it wasn' much savings. This was in January, she called them back about a week ago because she hadn't received any information she was supposed to get, confirmations, etc. But she looked at her credit card statements and had paid for the charge of the cruise. Cosco told her they had no record of her booking and there was nothing they could do for her. So in the end she ended up losing all of her money and not getting to take her vacation. Others have had similar experiences with all these type sites. It can even be less important things where you get on the cruise and discover the ports or itinerary changed, your cabin is different, etc. Some people even arrived at the ships to discover they had no reservation at all.
So my suggestion is to find a travel agent that specializes in cruises. As I said above, most agents will find you the same price and in many cases a lower price than the online discounters. But you will have a reliable source that will keep you informed of any changes and give you all the advice you need to take a safe trip and a nice trip. You just need to decide if saving a few hundred dollars is worth risking not getting to take your cruise at all. Some people have had good experiences with these sites, but I feel it is best to get a good agent to help you.
There are also sites that offer last minute discounts for cruises. The cruise lines offer them rates that are so low you are basically only paying the taxes and fees. But you need to be really flexible and not care what you are booking, as far as destination, line etc. This way you get on the boat really cheap. The problem here is that you have to book airfare, I'm assuming. In this case you will need to book your air close to the day you depart. This will be the point when it is the most expensive. So you may not be saving any money on your cruise because of the high cost of air.
These are just a few options.
Hope this helps!