Kaleid,
If you remove the homemade drip pan and face plate assembly you will see a 1/2 inch male pipe thread fitting underneath the dispenser, this is your soda water inlet fitting.
You will need to get a stainless steel fitting with a barbed end to connect to that inlet fitting along with a length of braided tubing which will connect to your carbonator. This also requires a special washer.
You will also need a carbonator, CO2 tank and regulator.
Let me do some searching for that fitting and I'll get back with a link.
You can connect a brass fitting to the the inlet if you wish to test it for leaks with plain water.
Just rig up a hose of some kind.
The other tube coming out the bottom is the drain tube for the ice bin.
Syrup goes into the top tank, I hope you got the float that goes in the tank.
Post some pics of the syrup tank with the lid off and underneath the dispenser with the drip pan off so I can see the fitting and float.
Show me a close up of the nozzle area where the soda comes out so I can see if you have the syrup orifice.