As has been mentioned, ideally your Human Resources department should be made aware of the situation and handle it.
If it is in fact your responsibility, you need to address the issue directly, quickly and politely.
Be upfront and request a private conversation with the individual. Ideally you should have a private office or otherwise a conference room/ect where you can close the door. You don't need to humiliate them, it's a private matter, keep it private.
Be direct and tell them what is expected of them; their hygiene has to improve. Maybe they need to shower before they come to work, use deodorant, wash their hair thoroughly; you'll know the specifics. It's going to be uncomfortable so just make it as brief, clear and direct as you can. There is no "nice" way to say "you stink", but you can make it as painless as possible.
Don't pull the "A lot of people have been talking..." garbage. You don't need to appeal to social proof in this situation, and you can make the employee feel alienated; like everyone's talking behind their back/out to get them/ect. It's not relevant or necessary and it feels like an attack. You're responsible, own up to the fact that it's you who's telling them they need to improve their hygiene.
If they don't follow up on it, send them home. Again don't make a scene, contact them privately, but they have to go home, and you need to dock their time. Nothing is going to motivate them like lost time and money. If they don't shape up, make it clear their future employment is at stake if they can't operate professionally.