The cruise ship itinerary varies from a 3 night cruise from Singapore to a 7 day cruise in Alaska or Mediterranean . All over the world, in hundreds of different ports, cruise ships are sailing continuously. Cruise ships are moving 365 days of the year. One voyage begins in the evening immediately after the one before ends in the morning.
Then it might be a day at sea or a port. and the next port and so on. One has to choose from the different itineraries from the many Cruise Line companies like Norwegian Cruise Lines, Royal Carribean, Disney, Carnival and many others. Each company have many ships of different sizes sailing in those countries of each region connected by ports.
There are seasons of cruising and then the ship moves to next region because of climatic conditions. For example a ship will run 4 months in Alaska up and down from Seattle. And in Winter will move down to San Diego, Hawaii or Carribean, sometimes sailing all the way to Australia & New Zealand. In winter season ship will cruise in warm countries of Carribean, South America, East Asia and in Summer they will move to cold countries of Europe, Mediterranean, Alaska, Canada, Baltic.
When in port one can go around ones own hiring a taxi, public transport or walk around the port when tourist spots are nearby. Second option is to go on pre-arranged tours by the ship itself, which are of 3 to 8 hours. This you can at the desk next to Front Desk, known as Shore Excursions. At the start of the cruise they will also have a presentation of the many tours available with slide shows and talk by their staff, so you can know what to expect and choose accordingly.
The Shore Excursion tours are divided in groups and travel together in the same bus. There will be a tour guide with each bus who will be responsible for the all aspects of the tour. These tours are mostly preferred as they are safe and guaranteed to come back to the ship on time. It might be cheaper also sometimes to book private tours by oneself but one can only if they have good reviews.