1. Make sure to do your research on the different cruise lines.
Carnival is by far the cheapest cruise line to sail on. They are who we always use and have always enjoyed our cruises with them. You can also get some good deals on other lines (Royal Caribbean, Norwegian, etc.) but they are harder to come by.
2. Look at the different rate categories.
Most cruise lines has the standard rate as well as some other rates that you can book, like state residents (they will sometimes offering discounts to those living in certain states), military, and past guest.
Also, Carnival has a rate called Early Saver. If you book your cruise a certain amount of time before sailing, you can get an outstanding rate. If the price drops within 2 days of your sailing date, you can get your price adjusted. This is the rate we always sail on because it gives you the best deal. The only downside to this rate is that it is a non-refundable deposit. So, if there is any chance you might not be able to go on the cruise, I would recommend not booking a rate like this.
3. Book an interior room on the lowest deck.
Most people don't spend that much time in their rooms anyway, so you don't need anything terribly fancy. The beds are just as comfortable and you will have the same service as the other decks.
4. Pay for things in advance.
If you plan on doing shore excursions, do your research before you and go ahead and book them before you leave. That way, you won't make a rash last minute decision that you want to swim with the dolphins for $200 per person.
Also, if your cruise line gives you the option, pay for your tips in advance. That will be one less thing to worry about at the end of the cruise when you have to pay your bill off.
The number one tip to getting a great price on a cruise is to do your research. Check out a website like CruiseCritic.com. They have tons of information for you right at your fingertips.