Well, the good news (or bad news, depending on how you look at it) is that the combination you have gives you great flexibility in how you set things up. Unfortunately, this means you have to think a bit about what your needs are.
The mixer you have has ten inputs with direct outs which is great. You interface has multiple inputs you can use.
The big questions are, first, how many tracks do you want to record at any one time and, second, what software are you using for mixing?
Assuming you will be doing all instruments and vocals yourself (i.e. recording one thing at a time), I'd probably just feed my mics and any instruments into the first few mixer inputs, then feed the direct outputs into the first few line level inputs on the Edirol. You'd use quarter inch TRS to quarter inch TRS cables for this.
I'd also bring at least two (maybe more) outputs from your computer via the Edirol into the last few inputs of the mixer, then use pre fade auxes to feed to the headphone monitoring, mixing your vocals/instrumentals from whatever channels you're using mixed with the returns from the computer. This would also use quarter inch TRS cables. I'd personally probably mix the recorded tracks in the computer software and just feed that mix to two channels on the mixer. However, you could bring more channels out and do some of the mixing on the auxes...your choice.
However, the thing is that with your combination of gear there are lots of other ways you could do it. Probably just time to buy some cables, dive in and try things.
Bob