HIya,
There are a few different possible options:
1. Plug in a 'permanently' fixed Micro USB cable - RichArcade in this other forum post has some pictures and videos showing a right-angle cable that might be more ideal than a regular cable that sticks straight up:
http://forum.tinycircuits.com/index.php?topic=2309.02. If you don't want any headspace, you could solder a power cable, or a stripped micro USB cable to a 2-pin JST for power and ground and plug this into the battery port. Here's a 2-pin jst:
https://tinycircuits.com/collections/cables-connectors/products/jst-sh-2-pin-connectorIf you like this option, you could potentially use the 2-pin connector on the battery that comes with the kit - you will just want to be very,
very careful not to cross or short the battery leads after snipping the 2-pin off. Lithium batteries can smoke and potentially explode when shorted.
3. This is the same process as #1 or 2, but if you ideally want a button or switch for the power rather than a cable you plug in and unplug, you could add in a switch to the wires. This might look ugly, but if you want a switch this would be an option.
4. Same as #1-2 where you would install a 'permanent' power source / cable, but you could use the IR Receiver that's on the MicroSD & Audio TinyShield if the enclosure around the TV isn't too thick (the IR chip is the black square at the top of the Shield), and if you have a spare IR Remote around. The TinyTV mode that uses a remote code to change channels/videos and toggle the screen power should be available as a setting on the Tiny Video Player kit, and you can edit the IR settings to work with whatever IR remote you have. Then you could turn the screen off and on using a remote. This might sound confusing if you're unfamiliar with the settings menu, but this would be my personal favorite option since you just need a micro usb cable and a spare IR remote. Here's the settings menu tutorial:
https://learn.tinycircuits.com/Kits/TinyTV-Tutorial/ (don't get confused that all the pictures show the tinytv, the tiny video player kit has all the same software and hardware minus the Tiny Remote and printed enclosure)
Let me know if you have any questions or need clarification on anything I mentioned. Would love to see how you're using the kit!
Best of luck!
-Réna