acetone degrades the structure of plastic, sort of eats it away. this allows the dye to take hold within the plastic itself. acetone dying only dyes the top layer of plastic, whatever the acetone has 'softened' up to accept the dye. think of it as tooth enamel and a soft drink... the acid in the drink eats away at the enamel, allowing particulates into the tooth where otherwise it'd be protected, then discoloration can happen or all sorts of things.
the recipe varies but is essentially a mix of HOT water (the hotter the better/quicker the dye takes), acetone, and the dye. rit dye comes in liquid and powder, if you use the powder make sure to wear a mask. its very fine, and you'll breath it in and have colored snot for a day or so. i did black and it really freaked me out until i realized what had happened.
also, acetone is a carcinogen. a mask is called for anyways. lastly, rit dye will stain most anything! its a cruel bugger. it can stain a sink also, especially when the misture has acetone in it (and if your sink has a porous surface, you've just colored your sink).
this google search should help out, the recipe and approach is basically the same: https://www.google.com/search?q=rit+ace
=firefox-a
edit: i forgot another important thing....
acetone lowers the boiling temperature of water. so, if your water is near boiling, pouring in the acetone will cause it to boil a little until the energy works itself out. this can cause a little splashing. so, keep this in mind and be aware of the surrounding area so you don't end up with splashed spots of color on teh counter-top.
doing this all outside is preferable, on a hot day if possible. it helps the mixture keep from cooling so rapidly.
and, very very lastly i think, acetone will not melt or eat at aluminum, the cheap baking pans in the grocery store are perfect for this. do NOT use a plastic bowl/vessel, the mixture will eat through it (like it does any plastic). well, not 'eat through it', more or less degrade the molecular structure of the plastic...