Where and how are exchange rates determined?

Typically on what the last trade was.

It all depends what I am willing to pay out (or what I think the currency pair is worth) and vice versa, what you think the currency pair is worth.

In the genesis moment, we might disagree until such time we agree and a trade is made.

The rate at which the trade is made would be the exchange rate. Exchange rates are reflective of the traded rate. When more trades are made, it is then reflective of the rate and the size of the trade taken into account. If a VERY large quantity was traded, the rate can move quickly, if a light trade occurred and someone tried to manipulate the market the exchange rate would average that in and a very slight increase/decrease would show.