To hatch your worm into a random/worm just raise your worm as you normaly would and when its 3 years old make sure it's very well the week of the official june tournament. If done correctly after Holly tells you about the tournament the screen will go black and then there will be a large cocoon in the center of the screen.

Tips: To get what you want, save on the 3rd week of June and keep hatching until you get what you want. Also work out on the traits that your worm is good at(a rock worm gains power easily so work on that)so your monster is really fast, strong, smart, etc. Have fun, I've gotten a lot of good monsters this way.