:
I'm not sure I know exactly how to use the Minkowski diagram. For
example, let's say you have a stationary observer and a moving
observer, and an event somewhere, for which the coordinates are x and
t in the stationary frame and x' and t' in the moving frame. How do
you get t', for example, from the Minkowski diagram?

You've got to be aware that the units of an xt frame have a different
"length" than those of any other x't' frame. All units are to be found along
a hyperbolic curve, one for space axes' units and another for time axes'
ones. This relationship corresponds to Lorentz-equations "singling out" a
space coordinate x' (t'=0) or a time coordinate t' (x'=0), ending up in
hyperbolic (x,t) correspondents.
Example in
http://home.scarlet.be/~pin12499/MyS...ntzObjects.PNG
at my SRT page
http://home.scarlet.be/~pin12499/paratwin.htm
with much more graphic stuff.

guido