How do you wire two lighting circuits through a time clock?

If you mean two separate circuits from different breakers, you will need a 2-pole time clock. The circuits will need to be kept completely separate, including neutrals. Remember that a time clock is just a switch operated by a timer and you only switch the hot wires.

The clock will be operated by one of the circuits. For this you will need the neutral of that circuit connected to the neutral contact of the clock. This is all rather simple if you can follow the wiring diagram provided with the clock. I doubt you can find a 2-pole clock at the local hardware or home improvement store. You may have to go to an electrical supplier.

I say this is simple and for an electrician it is. If you get the clock you need and it doesn't make sense to you in a minute or two you should not attempt to do this yourself. Crossing the hot wires or connecting the wrong neutrals to each other can create very unsafe conditions.