I live in Georgia and am putting a garage apartment behind my house. It is about 30 - 40 feet from the main house. I would like to know how many different trenches I will have to dig, how deep, and what utilities can share trenches. If I go with natural gas heat, I will need a gas line (3/4" plastic?), 3" PVC sewer, probably 4 AWG wire for electric (in 1" PVC conduit?), water supply (3/4" PEX?), low voltage (1" PVC for cat 6, cable, etc.?). There is a possibility I can run separate electric service from another pole to the garage if the electric trench will have to be too deep or not able to share a trench with another utility. Thanks.
I'd say that there are too many unknowns in regards to what your local jurisdiction mandates for burial and separation of utilities for anyone to answer with any certainty in your situation. What might be legal in one town may be illegal in the next town over, so the only sure way of knowing how you can legally and safely bury your utilities is to talk to your local permitting authority. I'm sure they have plenty of documentation for you to look through which should answer all of your questions.
If you just choose to blindly proceed without following guidelines and proper permits and inspections, you will most certainly not get a certificate of occupancy for your garage apartment, and likely you'll need to dig it up and do it again. If you're in the rare situation where there are no permitting authorities, I still suggest following guidelines of a nearby authority for utility burial, just for safety's sake.
If nothing else, for any non-metal lines you run in trenches not in common with a metal line, bury with it a marking wire so that utility locators can easily find your buried utility lines in the future.