So I personally am not made of money and NEVER expected to be able to sail again after my first time. It's a long story but my wife passed away and I had some extra cash as well as a need to plan something and heal.
Since then I have sailed a couple more times and will soon be on another trip. Here are my secrets.
Search, search some more, then search again. Don't just rely on the RCCL site in fact I recommend VacationsToGo.com The 90 day ticker is awesome if you have extra cash and want to get something really cheap and can easily get to a port or live near one.
Book with a travel agent. Vacations to go often has 50 to 75 dollars onboard credit they apply when you book through them. It's not a ton but everything counts and the onboard credit can be used for the tips.
Don't bother with drink packages, upgraded restaurants, or excursions. Pack a couple bottles of wine if you want something to drink (just remember that if you want to drink it at a restaurant they may charge a corkage fee which covers opening the bottle and providing glasses) and grab a 12 pack of soda to take with you. You are limited to 2 X 750ML bottles of wine and one 12 pack of soda. There is free food in the windjammer, main dining room, and a few other spots around the ship. And you can go ashore and walk around in the port area or venture into town for free, if you really want to shop find a local grocery store and look around to see what is interesting. You can easily take along some stuff for the beach, some fins a mask and a snorkel for swimming, or even a skateboard, surfboard, or bicycle to use while in port. https://www.royalcaribbean.com/faq/questions/prohibited-items-onboard-policy
Pack commonly needed medications with you. Take something along for allergies, pain, sunburn, cuts and scrapes, etc. If you have a sensitive stomach take some pepto or whatever your preferred substance is. While there are medical facilities onboard they are not exactly free so why run the chance of needing to stop in if you can prevent it. Same goes for nausea meds.
If you are driving look for places to park outside of the port area. On an upcoming sailing parking at the official port parking is 15.00 per day. I was able to book with a private lot with a shuttle ride to the port for 7.55 per day. Sometimes you can find lodging where they will allow you to park your car for free just for staying there and sometimes will have a shuttle as well.
If more than one person is traveling plan to drive. It sucks especially for long trips but to travel from many locations it's just cheaper. Yes there is wear and tear on the vehicle but you can carry your bags to the port for free, spend time in the port area without paying someone to drive you around. This is not always the case but most of the time will be unless you are traveling an extreme distance or have tons of direct flights from your local airport most of the time driving will be cheaper. And if you have to pay to check bags that pretty well sinks it.
Look at all your travel options. Yes driving with more than one person will generally be cheaper but I still look at flights and Amtrak when I make plans. For long distances where there is a direct route to the port city or nearby you may be able to take the train for less and you never know when a sale will be happening.
Shop around when looking for a room before sailing. Sometimes being a few miles further from the port will be drastically cheaper. When I travel to Galveston in the off season I get a room on Galveston Island, the rest of the time I end up staying further away because the room is almost half as much per night.
If you travel in early look for a grocery store vs fast food. Yes it's a convivence factor to buy fast food but if you are driving a long way get in a couple days early so you can have a day to relax. Take a small microwave or book a room with one included. It's easy enough to take a cooler as well if a refrigerator is not available. You can then still have a warm meal that won't break the bank. Also traveling with a cooler means you can make sandwich's and such while driving saving a bit more over fast food on the road, not to mention you can easily pick up healthier options if you want them.
Carry your bags to the luggage drop off area. The porters are not free, they work mostly for tips and while they will probably take your bag it's still best to at least drop them a few bucks for doing so.
Search for cruise's during off season's or when everyone else HAS to be at work/school. The summer cruises are always going to be busier because school is out. Not only will there be less kids on the ship while school is in session but there will be less people and usually cheaper fares as well.
DO NOT BOOK A CRUISE THAT TRAVELS ON A HOLIDAY LIKE CHRISTMAS OR OTHER LOCAL HOLIDAY. In the USA Christmas, Thanksgiving, New Years and Valentines day are ALWAYS jacked in the price category. Everyone has the same though of a romantic or family vacation and the cruise lines know it. Book the week before or after, while the date on a calendar is nice you can celebrate a little before or after easily. Plus if you really don't want to drive the flights to get to the port will be higher around those times as well. I am sure other holiday's will be similar.
Do lots of mock bookings. The advertised price on the RCCL site isn't always the same as the price you can actually book at. So do a mock booking and see if your age, job, state of residence, or Crown and Anchor Society benefit can get you a discount. Sometimes it's worth trying them individually as well.
Take a risk and go for the guaranteed room option. I have done it and the room was fine, yes it's a risk that you could end up near a noisy area. If that happens politely go to the guest services desk and mention that you hear a lot of noise in the room and they may be able to move you or give you a little onboard credit as an apology. Don't be a jerk, these people have limits on what they can do and they want to make sure everyone is happy but it's not a perfect world. If the ship is fully booked there isn't much they can do. Also if your category is fully booked they can't put you in a suite just because without you paying extra.
Consider interior rooms. Seriously they are almost always cheaper. So unless you plan to sit on the balcony every chance you get why pay extra for the room. They are all on the small side but lets face it most of the time on the ship will be spent around the pool, at a show, or eating. For an Alaska cruise I would spring for a virtual balcony or actual balcony for the views but I also doubt I would be in the pool as much then either.
Take along your own entertainment. I carry a tablet with some movies and TV shows on it as well as a Raspberry Pi with a bunch of games on it. Take a look at some of my basic tips and tricks for more information.
Honestly if you do a little legwork and shop around you can get a trip on RCCL for not much cash. If you have a rewards credit card you can even use that to help decrease the cost a little bit as well. But it does mean you will be doing less while on shore but lets be honest you can take a towel and go sit on the beach for nothing most of the time and if you want to snorkel you can buy that equipment and take it along for a lot less than paying someone else to provide it.