How are stock prices derived?

I understand supply and demand, but can’t figure out how the price of any given stock is specifically determined. For example, lets say stock A opens at $20, and throughout the day more shares are sold than bought. Therefore the supply increases, demand is declines, and the price level declines. But how does that price get determined? Does someone holding stock A say “I want to sell this for $20” but the buyer says, “I’ll give you $19.75”, and eventually they settle on, say, $19.90? The greater the volume throughout the day, the lower the price keeps going as it is always negotiated a bit cheaper than the last selling price?

I don’t know if this hypothetical negotiation actually occurs, so I won’t elaborate further. Someone please explain this.