Check on the websites, the cruise company's own & the websites of the various destinations. depends on where you are going, the Med ports of Florence & Rome, for example, are a little bit more difficult to diy as they are inland a bit, but the Caribbean ports are very slick, just walk off, take your time having a look around to see what's on offer, listen to other groups, butt in to suggest 'palling-up' with them, don't be drawn in to the hype & hassle, a favourite of ours is "We've been here many times, thanks we are just having a wander" & they generally walk away to bother someone else You can pre-bbok when you get on the ship but by then a lot of people would have booked online. If you cannot book online, get to the shore excursion desk as soon as you can. Some cruise companies send booklets out prior to the cruise.
I find typing in the name of the place into Google and checking out the various sites which appear is the quickest way. You can also see what excursions are on offer independent of the Cruise Line and maybe get some ideas and possibly save a lot of money.