The base should allow for most 2.1x5.5mm DC 12V2.1x5.5mm DC 12V Female Power Plug found on ebay. You can glue it down or double stick tape. You could also add a on/off switch to the back or top if needed the micro switch should work well. Mine will be daisy chained to multiple stands with one switch.
Step 1: Preparing the LED Strip
The LED strips can be cut into sections. Usually it is every 3 LED's, butt be sure to verify before cutting. You will want to cut as squarely as possible to avoid ruing the next set of leds. If you do cut to much and can't get a good solder point then move that piece to the very end where you only need to solder one side.
Step 2: Base With LED's
The LED's are very simple design. I will be matching the colors to the original sword light inside of the base. It will appear to glow as if powered for the lightsaber. The Flexible 12v LED strips work nice for projects like this. Just solder +/+ and -/- leaving the last tab open. Adding heat shrink tubing to the ends will help make a cleaner look.
If you don't want to solder these lead connectors may work. Have not used them so can't be sure. Make sure to order ones that match your LED's.
Step 3: Power
Since LED's draw very little you may have old cell phone or toy charger around that house that will work. You can use from 9V-12V and 2A for this setup. Here is one you can buy that should work.
I am in now way an electrical engineer so use caution or don't attempt if you're not sure.