I saw this post in the "ask me a question" thread and I thought it was a goof. I guess you were serious.
I am assuming that you want to record individual tracks simultaneously. If so, you are going to want to run cables from the channel insert connections on the rear of the Mackie to the 4 input connections on the Delta 66. I believe that in order to use the channel inserts as a "send" you need to push the jack in just until you hear the first click. Check your Mackie manual to confirm this.
Next you want to run cables from one of the Delta's out pairs (1/2 or 3/4) to your powered monitor speakers. Or even better, run from the outs on the Delta back to Line In #13/14 on the Mackie, and then plug your powered monitors into the Control Room out connections on the rear of the Mackie.
Plug your headphones into the Mackie's headphone connection and use the control room volume knob to turn off the speakers when you just want to monitor through the phones (e.g., when you are recording).
Assuming that you connected Channels 1-4 of the Mackie inserts to your sound card, then those are the channels you will use to hook-up your mics and/or instruments.
This will allow you to record up to 4 individual mono sources (such as mics) at one time. Using more tracks in your tracking software, you can do this over and over to record additional tracks along with the first four.
This should get you started. C'mon back if you run into specific problems, or have more questions.