Budget tips I can think of:
Book using
www.cruisecompete.com. They will give you quotes from several travel agencies, and you can choose the best quote (the price will often be the same, but the amount of on board credit usually differs).
Book an inside cabin. As a PP said, you won't be in your room much, anyways. Everything else on the ship is the same for you as the people who paid hundreds or thousands of dollars more.
Board early (around 11am), if you can. You can eat lunch on board the first day. That will save you lunch $$ elsewhere. Plus, your vacation starts sooner!!
Check the cruise line's alcohol policy-- some lines allow you to bring on a limited amount of wine, etc. Disney is unlimited. Carnival lets you bring on two bottles of wine per cabin, I believe. The lines will charge a corkage fee if it's opened in the dining room. We request two wine glasses from a random bar early on in the cruise and keep them in our room. We open the bottle there, and take the glasses with us to dinner. Slightly tacky, but eh, it works for us.
Remember that you will owe tips. They are between $10 and $12 PER PERSON PER DAY, so they can add up. Just budget them in.
Book excursions through outside companies, rather than the cruise line. You can save a lot of money. Just be sure that the company you book with has great reviews and will be reliable getting you back to the port on time. The ship will not wait for you.
If you are driving to the port, you can often find a hotel that will allow you to park your car there for the duration of the cruise for free. Check out cruisecritic to find suggestions on hotels for your particular port.
Not a budget tip, but if you are flying in, it is best to fly in the day before the cruise. The ship will not wait for you if your flight is delayed.
I hope these help! --Katie