The fastest cauldron in pottermore is the Copper Cauldron, which costs 25 Galleons.
Overheat it!
Click on the Potions section then choose a cauldron and a potion. You'll then be given a set of instructions to follow.
Swish and Flick! It's on the table next to the cauldron, click and just drag it up with your mouse.
First go into the hospital wing, and talk to Professor MacGonagle. She will tell you that someone in the room has a self-stirring cauldron, so go talk to the only other person in there, and she will ask you if you want to swap a couple of fanged frisbees for a self stirring cauldron. well, for me, she asks for a potion. not fanged frisbees. idk where to get them.
You should see a blue, yellow, and red little button beside the cauldron. The red one heats it up quickly and the yellow one heats it up but not as fast. The blue one stops it.
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There isn't a trick. Once you have chosen your cauldron and the potion you would like to make, you are given a set on instructions to follow in a certain amount of time. Read the instructions carefully and carry out each step for your potion to be successful.
I have a cauldron.
Some good sites for Harry Potter news and entertainment are fansites like Mugglenet and Leaky Cauldron. The best site overall for Harry Potter is Pottermore, an official Harry Potter experience. It opens to all in October.