How to test for a short to ground on a Macbook Air motherboard?

Bring it to a repair shop. Poking a motherboard in general is extremely dangerous for the components. You may further break things in the process.

If you do accept this risk and wish to continue... It would seem to be pretty hard. Apple, being Apple, doesn't label anything on the board. Based on some motherboard pictures on eBay, you'd probably want to use the ground pin from one of the other peripheral connectors (which have good data sheets with pinouts) and hope that everything is on the same ground bus (which I think is true). If you know/suspect what caused the shortage, see if any of its pins beep the meter. There should be one (the ground pin). If any others do, that indicates a short (unless there are two+ ground connectors, like on Thunderbolt).

TL;DR: You should probably have a repair shop check, and it's pretty hard to check it yourself.