The LCD literally plugs in to the front of the Typhon board. That's what the 16 pin header along the top of the board is for. You need to use mating connectors of your choice. The "standard" is probably to put a female header on the Typhon and a male pin header on the LCD. That's what I've done in the photos shown earlier in this thread.
As far as connecting the drivers - the Typhon provides two banks of signal pins. They're mushed right next to each other in the 8 x 2 header along the right side of the board. Starting from the bottom, the first four pair are 10v pins, and the second four pair are 5v pins. With buckpucks, you want to use the 5v pins, which means you'll be using the top four pairs of pins to connect the drivers to the Typhon.
First you need to make sure that you actually have dimmable buckpucks. The buckpuck datasheet has diagrams on how to connect various external dimming sources:
http://www.luxdrive.com/download/?dmid=1109
You want to look at either figure 13 or figure 14. The "issue" with buckpucks is that they want an inverted signal (i.e. 5v = off, 0v = on) while the Typhon follows the more conventional standard of 5v = on and 0v = off. So you have a choice:
1) You can wire as in figure 13, which is very straightforward and only involves connecting the signal line from the typhon to the CTRL pin on the buckpuck and making sure they have a common ground. If you do this, you'll need to fake your on/off times in the settings on the Hydra, because the buckpucks will basically flip the signal (i.e. when the Typhon thinks they're on, they'll be off). So if you wanted them to come on at 8 AM and off at 5 PM, you'd set an on time of 5 PM and an off time of 8 AM.
2) You can wire as in figure 14, which involves adding a resistor and a transistor to the circuit to invert the signal. This is a little more involved from the wiring side of things, but it would make the software more straightforward as you can just use the Typhon as nature intended.