How to move vertices while modeling? I used a plane to start to make a character. When I started to convert it into 3d the I can move any of the vertices on the global x or z directions, but I cannot move any of the vertices on the global y axis, even when the Transformation orientation is switched to global. 

A copy of the blend file can be found at:

https://www.mediafire.com/?2b7jks1q6dqy1bu

and here is a screenshot illustrating the issue.
I'm not quite sure how the mesh has got like this, but essentially I think the mesh has been scaled (in object mode, I think) so it has zero thickness (in the object panel the 'z' scale value is '0') which I think is why you can't move anything in edit mode. Any movement is being 'squashed' back to zero.

To fix this you can go to object mode, select the mesh and press Ctrl+A> Scale. This 'applies' the scale, resetting the scale values to '0' but leaving the mesh appearance unchanged.

This question may help, though applying scale can be a complex subject:

Why are the longer edges being beveled more?