First you need to find your hair dye - there are brands like Raw or Manic Panic that make deep purple shades like this. They usually come in bottles and the color is already mixed and ready to be used. (If your hair is long, you might need two bottles)
If you have dark hair, you will need to bleach it first so that the purple will show up more vibrantly. You can do the bleaching at home after reading carefully on how to do it, but I would suggest having that done at a salon to prevent any damage.
If your hair color is already pretty light (light brown to blonde) just work the hair dye into your hair according to package instructions and leave it sit for the recommended time.
You might have to play around with the time a bit, I usually leave the color in overnight to maximize that hold, but some people only need to leave the dye in for an hour or so.
Check out some Youtube videos about dying your hair purple. Those should help!