Here is a quick and easy way to get your carbon electrodes. These seem to be fairly more difficult to find or order and there are a number of people who simply use the lead from pencils but here is another cheap and easy source that is often overlooked. You can simply pull the carbon electrode out of the center of a carbon zinc battery. These are normally fairly cheap (about $1 USD/pack) and found at most stores. The main thing to look for to make sure you are getting the correct ones is the packs that say they are for low drain devices like so.
This was a pack of 8 for $1 at The Dollar Tree. You can also find the yellow Rayovac ones at most stores.
These have a plastic label on them that can be easily cut and peeled away with a knife.
Now you just peel back the crimped edge around the positive end with a pair of needle nosed pliers. The zinc sleeve is fairly soft and will bend easy.
Now you can remove the cap to expose the carbon electrode. Another easy way I found was to use a pair of metal tubing cutters to remove the top and bottom of the zinc sleeve.
Use your pliers to remove the carbon electrode from the manganese dioxide and carbon powder paste inside. Clean the electrodes with some Gojo or any other petroleum cleaning agent from the automotive section (the orange stuff works also) as the manganese dioxide paste is kinda sticky. The paste is inside a paper sleeve in the zinc. You can easily remove this if you cut the bottom off and use a dowel or the back of a pencil to push the paper sleeve out the top. It can be extremely messy trying to dig this out from the top!
AA batteries will have a 3/16″ electrode and D cell batteries have a 3/8″ as seen in this picture. So there it is quick and easy, now go play with all your electrical experiments you have planned!