The easiest way to tie-dye polyester is to use fabric paint, instead of dye. Two fabric paints that can be used for this are Dharma Pigment Dyes, which you can mail-order from Dharma Trading Company, and Jacquard Products' Dye-Na-Flow, which you can buy by mail-order or from some of the better crafts stores. Both of these fabric paints are described by their manufacturers as suitable for polyester. You can dilute the Dye-Na-Flow paint with up to 25% water; the Dharma Pigments can be diluted considerably more, with three to four times as much water as paint.

Another easy way to decorate 100% polyester is to make your own iron-on transfers, drawing or painting on paper with a special kind of polyester dye called disperse dye. Disperse dye crayons can be purchased at the local sewing store under the name Crayola Fabric Crayons. The colors look dull on paper, but are very bright once ironed on to paper. It's a little more difficult to paint your iron-ons, because you will have to mail-order the disperse dye to make them.

It is possible to do a true tie dye on polyester, but it's not at all easy. It requires not only that you mail-order the disperse dyes, but that you apply them according to the correct recipe, and then heat-set by steaming or in a pressure cooker. 

You absolutely cannot do successful tie-dye on polyester using the same type of dyes you would use for cotton, because cotton dyes will just wash out of polyester. Using fabric paint or the special polyester dye solves that problem.

Also, I have a 100% fleece polyester blanket that is blue that I want to make green and brown. Is it possible?

Yes, you can use yellow or green disperse dye dye or fabric paint on a blue blanket blue in order to make green; use brown or rust to make it brown. Both dyes and fabric paints are transparent, so the original color will inevitably show through, but both green and brown are colors that can be made on top of blue.
For more information, see:

• Dyeing Polyester with Disperse Dyes

• Iron-on Fabric Crayons for Synthetic Fibers

• Fabric Paints: a different way to color fibers

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