Does screen sharing work when not on the same local network? Does screen sharing (System Preferences > Sharing > Screen Sharing) work when the computers are on different networks?  For example, if computer A is using Wifi in Texas and computer B is using Wifi in New York, will this still work?
Yes. And you can make it work through most firewalls if you're both using Messages. Messages will broker the handshake to start the session and then turn it over to the screen sharing app.

Start up Messages and make sure Screen Sharing is enabled:



Find your buddy in your contact list in Messages and click on them. Then select Buddies -&gt; Share My Screen with Buddy... or Buddies -&gt; Ask to Share Buddy's Screen... from the menu bar to initiate a screen share session. You can share control with these sessions.