My cousin lives in Ohio, I live in Texas. We want to ship a pistol from him to me. There is no sale involved, simply move the gun from his home to mine. How do we do that? Do we need a FFL here...or there... or both places? Is there a fee involved (other than the shipping costs?) What kind of paper work is needed? What is the best way to ship...mail or UPS?

As you can tell, I know nothing about this and have a lot of procedureal questions. If anyone knows the answers, or ccan point me to the right place, Id really appreciate it.

You must go through an FFL on the destination side.  You do NOT need to use an FFL on the source side of the transfer.

In other words, whoever has the pistol now can send it directly to the FFL.  The receiving FFL than does the rquired paperwork to transfer it to the receiver.

Shipping will be required, next day air, by most common carriers.

The receiving FFL will charge some fee, most likely.