Once it's at the end of its lifetime (usually after three years), the implant is removed at a gynaecologist's clinic. Again, you'll be given some local anaesthetic over the area. The doctor will then make a tiny cut in the skin and remove the rod.
You can get pregnant soon after it's removed. Unless that's your intention, be sure to either get another implant inserted, which can be done at the same visit, or use other types of contraception.