Djinn8 said:
Serious Sam. If that's not an FPS trainer I don't know what is.
+1 for this. She will learn very quickly the principles of strafing, and the game is just so much fun.
Also, Halo PC might not be a bad idea - again, a fun game, and the slow projectiles of the majority of the enemies will reinforce the strafing message from Serious Sam.
I'd personally say that UT and Quake might be too fast-paced and too reliant on mechanics such as bunny-hopping and double-jumping that may not be immediately obvious, or relevant to most mainstream shooters, though then again they could just be good fun and the presence of slow projectiles as well as instant hit weapons gives variety.
Modern 'so real' shooters would be unforgiving to a newcomer, I would expect, especially online. If she's struggling with the principle of strafing then they aren't going to help with that as it's not instinctively obvious that it would be of benefit against bullets if you haven't programmed in that reflex.
Playing online, say in TF2, might not be too bad an idea - point out how other people avoid incoming projectiles, see the benefits of not tanking all the pain, learn from example n all that.
My first FPS was Goldeneye, which I completed before learning that there even were buttons for strafing. Then I played some Jedi Knight, which didn't have mouse support and again didn't advertise the idea of strafing, but the slow blaster bolts introduced me to the idea of trying to avoid incoming fire. Playing Goldeneye with friends again, having discovered the joys of the C buttons and running circles around each other, I finally learnt the power of the strafe. Everyone needs to start somewhere - perhaps the key is making her understand the point before learning the action.