If you're looking for a quick way to get this, I recommend getting a ship that has passenger space - your default ship from the start has it, but If you've moved on to another ship you found, earned, or stole, make sure the new ship has a module that falls into the All-in-One Berth, Living Quarters, or Mess Hall class, no matter what company manufactured it. These all grant 2 passenger slots each.
Mission boards in cities, colony settlements, shipyards, and semi-randomly generated civilian settlements on moons and planets all tend to offer these missions, usually with a generous time requirement, and they're as simple as accepting the mission and proceeding to the location indicated on the quest. You don't need to do anything special to deliver the passengers, just land and walk into whatever location was indicated.
If you're handy with combat, accepting the missions from mission boards for killing a specific target or ship can also be handled quickly. You can accumulate quite a lot of these at once from mission boards on a variety of planets, moons, and stations, and then knock them out quickly with whatever's closest. These almost never have time limits attached either, so it doesn't matter what order you carry them out.