Possible to raise the babies? YES. Have I heard of anybody doing this with zebra gobies before...no.
How do you start? I suggest Wittenrich's Breeder's Guide to Saltwater fish to start as reference material. Also look into the possible fry food choices as well (personally, I think copepods are the best food, but they're harder to rear than rotifers and BBS). Finally, check out the net to see if anybody else has done it, MOFIB might have a few threads on there. You are talking about Ptereleotris zebra, the zebra barred dartfish, or zebra goby, correct?
You probably won't be able to rear this first batch of eggs, as you don't have the necessary food items or setup for the babies.
What do you do when you get the necessary stuff? Most of that will be covered in Wittenrich's book.
Here's my untested idea on how to raise P. zebra eggs to juvie stage: grab eggs, hatch in either a kreisel or round black tub, and stock water with copepods of the Parvocalanus/Acartia species, and also with Isochrysis galbana, Tetraselmis, and Nannochloropsis microalgaes. Maintain copepod and microalgae levels in acccordance with Wittenrich's book, and hope for the best. Also, constantly drip in new water slowly throughout the project. Try to get them on rotifers and BBS ASAP, approximately a week posthatch. Once you get them past metamorphosis, then your only job is to keep up water quality, and feeding.
Look into other dartfish and firefish breeding logs, you might find similar species, which will help you find the answers to your questions. Good luck!