We have been on 9 cruises around the Caribbean and I have loads of tips, but let’s just start off with 3 things to do right away, as soon as you have booked your cruise.

Travel documents.
Do this one right away. Many regions will require that you have a passport in order to disembark from the ship, so don’t postpone your passport application or renewal. I have a friend who checked her passport a month away from the cruise date, and it was due to expire and she had to send in the renewal, plus pay an extra fee to expedite the application and it arrived only days before she was set to sail. So, do it now.
Even if a cruise didn’t require a passport, I always carry one so I’m prepared if something unexpected happens.
Book your pre-cruise hotel.
Yes, you heard me. Plan to arrive the night before your embarkation day. Ships run on a tight schedule and they will not wait for you. So, put a night’s stay in a hotel in your budget. This will give you peace of mind in case of travel delays. We have turned this into a reunion time with our cruising friends, meeting up the day before at an airbnb or hotel, to reconnect before we get on the ship.
Get your house-sitter, pet-sitter, and childcare if needed, lined up with alternates.
Whatever you need in place at home, to be able to relax and enjoy your cruise, start lining that up as soon as you know you are going on a cruise.

Once you have these things in motion, then you can start to look at the cruise website for the excursions you might want to go on, getting in shape so you can carry all those bags to the cruise ship, shopping for some fun clothes, and planning out your packing list.