[meatmanek]

There are 3 popular styles of holonomic drivetrains:

Omni-wheel/Trick wheel drive:

This drive type uses trick wheels that are typically aligned perpendicular to each other. Each trick wheel allows unrestricted motion in one direction, and can be powered in the other direction. Most teams have 2 wheels driving the robot forward and two driving it sideways, though some three wheel drives, with 2 driving forward and one driving sideways are commonly seen too. Though I haven't seen a robot in FIRST with triangular omnis, they can be found outside of FIRST. (Each wheel is mounted at the point of a triangle, and each is aimed 120 degrees to the others)

Mecanum wheels:

Mecanum wheels are similar to omni/trick wheels, because they have rollers mounted around the edges. On mecanum wheels, however, the rollers are angled, rather than perpendicular to the wheel. A mecanum wheel is driven in one direction, and allows free movement at 45 degrees to the driven direction.
Mecanum wheels work on the same principle that roller skates work on. In a pair of roller skates, to drive yourself forward, you turn the skates at an angle and push them sideways. Similarly, in mecanum wheels, you turn the rollers at an angle, and push them forward or backward. Each wheel on a side of a mecanum drivetrain has oppositely angled rollers - one will have the rollers pointing in, one will have them pointing out. By driving your front wheel forward, and your back wheel backward, you force your robot to go sideways. Otherwise, the driving is very much like standard tank drive.

Swerve or Crab:

This is a more difficult holonomic drivetrain to build. In Swerve or Crab drive, each wheel is powered on its own, and each wheel can be steered independently. The difficulty of this drivetrain lies in the choices you have to make: How many wheels you want to drive (swerve/crab can be done with 2 driven wheels and a few stabilizing casters), the range of motion of each wheel (should each wheel be able to spin freely, or will there be a limit?), and how you will steer each wheel.