Your luggage will have a colored tag on them that they give you the day before, you tear part of it off and when they call that color, you go down and locate it. When cruising out of Miami on Royal Caribbean, they have a luggage pick up area very much like at the airport, you find you luggage as it comes around and off you go. They will call the color once you luggage is put on the belt, so no need to get off any sooner, it won't be there. Other lines, will have the luggage sorted by color in a huge room and you'll need to locate it and go from there.
And, if you need to be off the ship as early as possible ... say you have a flight before noon and want to make sure you have plenty of time to get to the airport ... let the front desk know as soon as you get onboard that you want to be assigned one of the first colors that will be called to disembark.
Then ... and this is not official ... but some cruiselines, such as HAL, really never even check those tag colors as you walk off the gangway. As soon as you hear colors being called ... even if your color has not yet been called ... just proceed to the gangway and head off the ship. No one will even care what color your tags are. I've done it several times after being told by a cruise director that I could really get off anytime after the ship has been cleared. Same holds true if you want to be one of the last to disembark ... such as in the case where you are being picked up by a friend at the pier, and maybe they can't get there before late morning ... you can always ignore it when they call your color, and just wait until they make "last call" to get off. They will clearly make the announcement that ALL remaining passengers must now disembark, and that will be your cue to head to the gangway.