Not everyone can afford a space worthy vessel or they don't need one often enough to bother with purchasing one. To fill the gap a few companies developed passenger cabins which can be fitted inside the standard cargo hold allowing any Captain with the appropriate cabin to pick up and deliver passengers.
How to get started
You will need to purchase a passenger cabin. There are several stores that sell them and some are crafted by players. This profession is very lucrative with a high X.P. and credit pay off. The other nice thing is almost every planet hosts a Passenger Office. For specifics on how to transport passengers see the how to transport passengers guide.
A passenger cabin is all that is required. There have been some recent advances in this field with a newly developed passenger frame which allows a Captain to equip special pods and haul groups.
DOs and DON'Ts
Try to get multiple passengers at one destination.
Don't have single deliveries to a distant arm of a galaxy.