Today I decided to add a battery to my T-Deck. A search brought up batteries ranging from 600mAh to 1560mAh, so I chose the one with the most capacity.
First, I tried charging it, and when I was successful, I attached the battery to the T-Deck with double-sided tape.
Next, I got out the battery connector that came with the T-Deck. I soldered it to another set of wires, wrapping the connection with electrical tape, since I didn't have any heatshrink.
After that, I soldered those wires to a battery connector lifted from the same phone the battery itself came from. Finally, I secured the battery connector with hot glue and used hot glue to secure everything else for good measure.
Next time I go to the hackerspace, I plan on building a case out of laser-cut acrylic.