If you want connect the ADAT to the PC, you need an ADAT interface in the PC (such as a RME9652). Each ADAT optic fiber carries 8 channels and you will need one for in and one for out.
The ADAT interface has embedded clock, so the very same optical fiber server for the purpose of syncing the ADAT and the PC interface. You have to set one as master and the other as slave. In this case it does not matter which one is master, but I'd suggest the PC card to be master, so it can work without the ADAT switched on. If you want the opposite, set the ADAT as master.
There is an optional connection called ADAT Sync, a 9 pin D connector. The wordclock syck is already done with the optic fiber, but using this connection allows also transport control.
If you want to connect it to the mixer, you need ADAT interfaces or TDIF/ADAT adapters for your mixer (I believe it uses TDIF). Just connect it as described for the PC. Then the mixer would be connected to the PC, also through ADAT connections.
A third option is to use an ADAT router to connect the PC to the mixer and the ADAT.
In any case, only one thing must be set as clock master and the rest as slave.