Just as in applying your purple contacts, you should always wash your hands before removing them as well. And just like in applying them, avoid soaps that contain any chemicals that can be dangerous if exposed to your eyes.
To remove your purple contacts, you can either look directly up, or to the side as you pull down on your lower eyelid and with a finger slowly and gently place it on the lens in the white of your eye and remove it by ever so slightly pinching it.
It is best to not have fingernails when doing this, but because that is not always possible, the more practice you have at it the easier it will no doubt become.

If you have hard purple contact lenses you can remove them by placing your hand with palm faced upwards, lean over it to where you eye is directly above it and open your eyelids as much as possible.
With your other hand, use your finger to pull on the skin of your eye’s outter corner out (towards your ear) and blink. It should if done properly come right out.
There are devices, such as plungers that you can get from your Doctor, that you can use to remove contacts if you are having problems or are squimish at first about touching your eye.
Since purple contacts will probably not be worn everyday, it can be common for people who use them to not be as used to wearing contacts and touching their eyes as regular contact lens wearers might be.
There are reports of people having their contacts dissapear completely behind their eye and become “lost” which is not possible, but it is possible for the contact lens to get so far back there that you would have to visit a Dr. to have it removed. This typically happens to people that are very new, but is not extremely common.