Very carefully. You can screen capture from the Android SDK, which is using ADB to connect to the device. Unfortunately, as Bundyo has mentioned, the 770 is memory constrained, so even trying to connect using ADB is tricky; trying to get the screen capture requires lots of crossed fingers and chanting.

I suspect one of the first tasks to make this stable on the 770 will be to implement some sort of swap file. If the memory architecture hasn't been altered too far from a stock Linux build, that might not be too difficult to do. I haven't looked into it yet, but I hope to find some time in the next couple weeks to see what is there and find out what is possible.