I can help explain how it works, if you'd like. But first you should know a few things.
1. Everything is lethal, it's just the amount that dictates when it's lethal. The dose makes the poison. You can die from drinking too much water, for example.
2. "Natural" has no bearing on health. Nature has no need to be safe or healthy for humans, it has no intent. It's just the way it is.
3. Artificial has no bearing on health either, it just means someone mixed chemicals in a lab as opposed to taking chemicals out of a plant/nature (more or less).
4. Origins make no difference when you're talking about chemical makeup. H20 gotten from a plant is the same as H20 gotten from blood, ya know?
5. Fluoride is one of the most heavily tested chemical ever. We know this stuff backwards and forwards.
Okay, given that, here's the skinny. The fluoride in water is in tiny amounts. Even assuming absolutely everything you eat or drink has a cumulative amount, and you add all that together, you're still going to be fine unless you're in an environment where the dose is much much much higher. Don't swallow loads of toothpaste
and which Foxi4 pointed out, it's still not going to hurt you (well, toothpaste has bitterants so your body won't like it, but that ain't fluoride's fault).
So, what actually happens? It gets in your teeth, protecting your teeth from the inside out. Teeth-rotting bacteria can't handle the stuff (more or less). You brush with fluoridated toothpaste to protect from the outside, and water fluoridation ensures you have a line of defense within your teeth as well. Genetics plays a part in whether your teeth are more susceptible to rot or not, So, drink fluoridated water and brush/floss your teeth and you help give your teeth the best chance they'll have.