I am wiring 12 Leviton dimmer switches to light up a series of 12 halogen under cabinet hockey puck lights. I am bring power to the first switch through a 14-2 wire and using a pigtail to conduct power to the second switch same with the 3rd and so on. That way each switch in the series can only be turned on when the switch immediately before it has been turned on. When I opened the box of switches, the wiring diagram shows a black, white and a green (ground) wire. Every switch has two black wires and a green wire. I assumed that it would be okay to wire each switch the same by using the wires with ID markings on them as the hot wire and the wires without marking as the white wire. When I wired it up that way the first switch didn't turn on and none of the others would come on. What is wrong?

You cannot wire dimmers in series and expect circuit to operate.
Problem is not 100% clear. Add a comment and include more information.

1) You have 12 dimmers.
Each dimmer has 2 black wires and a green ground wire.
The 2 black wires tell electrician that the dimmer wires are reversible.
One black dimmer wire connects to Hot from breaker, and the other black wire connects to wire going to Load (halogen lights).
If power passes through each dimmer going to next dimmer, the circuit will not work.

2) Unknown what you are replacing. Are you replacing 12 switches with 12 dimmers? Or maybe replacing 1 switch with 12 dimmers.
Number and type of devices being replaced is not known. And wires to each of these dimmers is not known.

3) You have a single 14-2 wire going to all 14 dimmers? Or does each dimmer have a different 14-2 wire?

4) You want to wire dimmers in series? So you want power to flow through one dimmer and control next dimmer?
You cannot wire dimmers in this manner and expect circuit to operate.
You can wire ordinary switches in series, but not dimmers.

5) Typically dimmers and switches are wired in parallel.
The Hot wire connects to one wire on each dimmer.
Since your dimmer has 2 black wires, the hot connects to either black wire on dimmer.
Then a jumper wire is added to connection, and the jumper wire carries power to next dimmer, and so on.
In this manner, each dimmer receives 120V potential. And then wire going to load connects to other black wire on each dimmer.