You are familiar with sh% then. For example if TNT has a sh% of 15 that means on every 100 shots he takes we expect him to get 15 goals. Sh% is a function of Goals/Shots. For GSAx (Goals Saved Above Expected) instead of applying sh% to a player, it gets applied to type of shot + location on ice where shot is taken. Instead of TNT having a sh% of 15, Wrist Shot from the Right Circle has a Sh% of say 10%. That is every wrister from that spot on the ice across the league. You then take the decimal for that (0.1) and over the course of a game, you add that up. So if there are 10 wrist shots taken from the right circle, that would be 10x0.1 and get you 1 goal. If your goalie saves all those shots, they would have 1 goal saved above expected because we expected 1 goal out of those 10 shots.
Basically you are replacing a players sh% with a % that is (Type of Shot + Location) and then using the decimal point to cumulatively count up the value of those shots. League wide shots on average shots are usually worth like 0.1 goals per shot taken (roughly) so over the course of a game where a team shoots 30 times, you end up with 3 goals on average. If your goalie allows fewer than 3 goals, that gets subtracted so they saved say 1goal above expected. I am using simple math here because usually you see an GSAx at like 3.27 or something like that.
Hope that helps. Just think of Shot Type + Location as a player and apply sh% to that, then add that up over the course of a game. There are more complicated GSAx formulas but they all basically have this underlying them. Some take into account individual players taking the shot or shot speed, or pre shot movement etc... but they still look at Location and Shot Type.