The recipe for preparing a home-made supercapacitor can be find at
Newer versions have 800 F of capacitance, 1.2 V voltage and 6 A of short-circuit current.
You need only some chemicals from the kitchen, such as water cleaning filter’s active carbon, sewer cleaning liquid (NaOH, but KOH is better), iron mesh, epoxy glue, shade cloth or paper for membrane and an empty Tic-Tac case.
Other electrochemistry experiments are here: