Fortunately this past Christmas my friend Andrea taught me how to dye in the microwave! So this was all I had to do:
First I soaked the sock in some sodium bicarbonate (soda ash) from the hardware store. This enables the fabric to absorb the dye and "fixes" it. I put about a quarter teaspoon of Dharma Trading's turquoise blue dye in a heavy zip lock bag.
Next I mixed the dye with about a quarter cup of warm water until it was well dissolved. I put both the sock and scarf in the bag, closed it, and squished the bag for a few minutes to coat the scarf and sock evenly with the dye.
Then I mircowaved the bag for two or three minutes, checking to make sure that the bag didn't fill up with too much steam and explode open (you have to stand and watch, just like microwaving popcorn).
Then I just rinsed in the sink, and threw both the items into a hot wash in the washing machine with a little Synthropol (textile dye detergent) to finish! Professional dyeing has never been so easy!
So now I have two blue socks, and a blue scarf as well, and I am very happy. :)
In my opinion, vat dyeing (on the stove or in the washing machine) produces darker and richer color that lasts longer. But for a small job like this, the microwave saves a lot of chemicals, trouble, and mess. Which means, more beauty for less work! Enjoy!