Welcome to TRS
Key off
Use volt meter or test light
Use alternator's metal case as the ground for all tests
Put volt meter on B+ terminal, the stud/nut terminal on the back of alternator
Should see 12volts, if not MEGA 175amp fuse on outside of engine fuse box is blown
Replace it before any more tests
Unplug the 3 wire connector on alternator
Test Yellow wire
Should see 12volts, if not 30amp ALT SYS fuse in engine fuse box is blown
Test light green wire
Should see 0 volts
Turn on the key
Should now see 12volts, if not CAB FUSE BOX fuse 15(7.5amp) is blown
No test for white wire but make sure it got plugged in correctly to it single spade terminal on alternator
If all wires test OK then plug back in 3 wire connector and start engine
Battery should show 13.5volts to 14.8volts, if not the new alternator is bad, period
Charging system is very very easy to test, just 3 wires, no mystery
Alternators on the other hand can not be tested, well at least by any auto parts store I have ever been to, they either work in your vehicle or they don't
I have read recent posts of people havng to return 2 or 3 new alternators to get a working one, I would change brands after the first bad one out of the box, lol