First you must go to the ender portal and put all the ender eyes in it, then you go through it. Once that's done, you must kill the ender dragon. When you see the portal back to the normal world, you will also see the egg on top. You put a piston next to it and use redstone and a pressure plate, lever, button, etc. to activate the piston. When the egg is pushed, you walk over to it and pick it up. Now you have your dragon egg.
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fire charges
The ender dragon drops it when defeated
kill the ender dragon
There's no spawn egg for enderdragon.
you cant yet the egg is just for decoration right now