Well, to a certain extent the washing care depends on the type of yarn you used, but unless it is wool I would wash it like this.
1. In your bathroom or kitchen, have some laundry detergent next to you and run tap until water comes out pretty hot.
2. Wet clothing in water then dip fingers in detergent and gently hand wash item. If the dye is going to run you will know pretty darn fast as the hot water and detergent start bringing out the "loose" dye.
3. Rinse out detergent and keep repeating step 2 until you are no longer seeing discoloration of the water/suds when you wash. Do not be discouraged if it takes a while - I had some purple silk that was so impregnated with dye it took almost 20 minutes of washing to reach a point where the water wasn't colored anymore - and the silk is still purple
4. Dry as appropriate for the fabric/yarn being used. I usually roll dry in a towel for my delicate stuff.