Is there anyway to network two wireless laptops without using a cable so I can use files on the laptop in the study while working in another room?

Yes, if you have a wireless access-point/router and both laptops have wireless network adapters you can configure a wireless network in infrastructure mode. Lacking an access-point, both adapters can also be configured ad-hoc for a wireless network. Instructions for doing either is dependent on your specific hardware which was not specified.

There's also "sneakernet" where the files are copied to removable media for use at a second computer and then later synchronized with the originals on the first computer.

If you have a wireless network setup that should be easy, but if not you just need to create a AD-HOC network on those 2 wireless laptop...