I fairly new to blender and i'm trying to move a specific face on its own. When I have the face selected and use the move controls, it tugs the surrounding area with it. I was doing it before but I think I accidentally hit a shortcut, and now it no longer responds this way. How do I fix this?
I think that you want to duplicate the face. You want to move the face without affecting the rest of geometry. To do this select the face and press shift+D and place your face where you want.
After you have duplicated and you want to delete your original face, press X to delete and select Only faces.