I've been dying my hair for about 20 years so I hope I can help. After you have left the color in your hair for the recommended time that the product recommends (10 min., 20 min., 30 min., etc.), you get into the shower. Get your hair wet with enough water so that the color mixture in your hair becomes somewhat diluted - then act like your using the diluted color to "shampoo" your hair. If you just tried to rinse out the color without this "shampoo" action, you probably wouldn't be able to rinse the whole color out (it gets thick as it sits in your hair for the 10 - 30 min. time period). You want to get all the color out so the coloring process will stop.
Once the water runs clear (after a few minutes of "shampooing"), then use the conditioning product provided in the box. You don't want to use real shampoo after coloring - you'd wash out the color you just put in! The conditioning product provided helps stop the coloring process and adds enough softness to your hair. Leave this conditioner in for a few minutes (I usually take this time to shave my legs - this takes at least a few minutes!) and then rinse out the conditioner completely.
Now you're ready to dry and style your hair as usual. I would also recommend coloring your hair on a day when you can wait about two days (or 48 hours) before washing your hair with your normal, real shampoo and conditioner. This waiting period should also help prevent the new color from washing out too soon.