On the port of call days many passengers wake up early and are at breakfast when the lines open. Many ships serve breakfast earlier on port of call days to accommodate guests with early shore excursions or the guests who want to get off the ship quickly. I have always felt that breakfast on a port of call day is rushed and many crew are stationed in the buffet to make breakfast a quick process.
As your ship gets closer to port, you will probably start to see land in the distance or up close. After breakfast or before breakfast (for some) many passengers who are not getting off first will be on the outside decks watching the scenery go by as the ship docks. I am always one of the passengers that eats breakfast and then I go and find a spot on the outside decks to get pictures of the port as the ship pulls in.
If you are taking a shore excursion or shore tour that is early you will want to make sure you are ready to get off by the time the ship is docked. Many passengers who are in this situation are usually waiting on one of the bottom decks in line to get off. Make sure if you are taking a shore excursion or tour that you give yourself plenty of time to insure you arrive to your excursion on-time. You don't want to miss your excursion!
During your day in the port of call make sure you are aware of the time and when you are required to get back on the ship. During your day in port, depending on what you do, you may have time to shop, take pictures, go to the beach, or take a shore excursion.
When the time to get back onboard approaches the line on the pier to get back onboard the ship will probably grow. Passengers may have to wait anywhere from 15 minutes to an hour. The line is so long because cruise lines scan guest cards and usually have a security checkpoint set up that all guests have to go through.
Your cruise ship may or may not wait on late guests. Typically once the ship has pulled away from the pier it is not going back to get any passengers who are late. If a guest is lucky the ship will go back for them or wait on them. Right before the ship leaves port you may see "pier runners" who are running to make the ship before it leaves.
Typically after a full day in a port of call the ship has many "dead" areas because most guests are tired from a long day in port. Usually the main dining room is a little less full and onboard hubs have a little less people.
Make sure you know your ship's schedule for the day in port, make sure you stay on ship's time, and make sure you give yourself plenty of time to get back onboard. Be back onboard by your designated time and watch the pier to see if you get to see anybody try to run and catch the ship!