You will need:
Electric oven, not gas oven. Sheet acrylic releases some fumes when heated and gas oven might explode, causing injuries and damage. So make sure oven is electric before attempting this.
Pair of Oven gloves, they are essential, you will have to work fast and oven mitts and towels are just not good enough of a solution. Trust me, I made mistakes so you dont have to.

Baking paper, this is self explanatory but: they are there so things you bake (sheet acrylic or cookies) wouldn't stick to your baking tray.

Obviously some sheet acrylic

Safety mask, because of the fumes, it is not a necessity but better safe than sorry. And also they are so cool, you can paint on it and wear it as a accessorise later. I have a collection and love them all

Some old wooden clothes pins, they are always handy no matter what you are crafting
Some tongs, don't use ones you already have for barbecue, fumes, heating the plastic and all that jazz is just not that healthy so buy a new ones just for crafting.
Some felt, to prevent scratches and sticking to the mold
Mold, if you want to make a bowl use the bowl if you making a hat use a hat. The point is, you will get the exact same replica of your mold so be careful what you use.
And Dremel tool, if you don't have it and want to craft anything, go buy it, it is an absolute necessity.


Now, we make something:
Preheat oven to 140*C
While the oven is heating up take out baking tray, cut out baking paper and put it on the tray
Cut out adequate piece of sheet acrylic
Put it on the tray and paper and elevate one end with clothes pins so you can see if sheet is pliable enough

Now stick all of that into the oven, 140*C for about 12 minutes
For that time cover your mold with felt,and make sure everything is pulled tight and secured in the back with safety pins.
Now, when your sheet is soggy take it out, put it over the felted mold and work very quickly.
You will end up with something like this

Now use your Dremel tool to cut off the excess acrylic, smooth of the edges and finish off.
And if planned build it into part of your costume.
You might need some practice so my advice is to start on something small and easy like bowls, cans and mugs and gradually build toward more complicated stuff.
Good luck and have fun