This one image in the link above pretty much sums up the practical use of how to enter that info:
We live in a non-cartesian world though! (although its pretty close tbh)
Don't forget that dimension 4 is ct (speed of light multiplied by time) but has a metric of -1 rather than 1.
I'll stop being a math troll for a second:
The strange part is how they setup the orientation of the axis. Mathematically if X is the dimension to target a positive Y means LEFT position. But many times people (who write software) define positive Y to be RIGHT. Positive Z will be up regardless.
If you look at the diagram (0,0,0) is the intersection of the axis. So image you are sent there and are looking out along X (blue, traveling down and left --thats a positive X distance), positive Y will be to your left, Negative Y will be to your right. It can be flipped, but you have to take care with 3-d ballistics to make sure the angles in your trig functions are correct because rather than 30 degrees it could be 210 degrees!
Bottom line just find out if left or right is positive..
This is a standard X,Y,Z axis. It looks like Y+ is right. But since we "look" along "X" the axes is from the target's position, not the shooters. It may seem like semantics, but trust me, lining up these things matters in the math.