Maya's dual-monitor support is kinda wiggy sometimes. It's easy enough, though, to simply move windows over to your second display. Depending on the task at hand, I often move my Outliner and Hypershade windows to my second display to maximize viewing areas.

Another thing that I like to do is open Maya on one display and then Photoshop on the other one. Then, I can paint in Photoshop, quickly switch over to Maya to update the texture, rotate the model, whatever, then move back over to Photoshop to continue painting.

Also, since I do a lot troubleshooting of scene files, I like to open the Script Editor on my second display and expand it to fill half the screen. That way, I can see everything streaming as I work.