Stock prices are set by bidding. In principle, a seller will say, "I want $80." If he can't find anyone willing to buy at that price, he'll either decide not to sell after all, or he'll lower his price. Likewise, a buyer will say, "I'll pay $70." If he can't find anyone willing to pay that price, he'll either decide not to buy or he'll increase his price. For most stocks there are many buyers and many sellers all the time, so there's a constant interplay.
The typical small investor has VERY little control of the price. You say, "I want to buy 10 shares of XYZ Corporation and my maximum price is $20." If the current trending price is below $20, your broker will buy it for you. If not, he won't. You normally have some time limit on the order, so if the price falls within your range within that time period, your broker will buy. That is, your choice is basically to buy or not buy, or sell or not sell, at the current price. You have little opportunity to really negotiate a better price. If you have a significant percentage of a company's total stock, different story.
In real life, most stocks are being traded constantly, so buyers and sellers both have a pretty good idea of the current price. If the last sale was ten minutes ago for $20, it's unlikely anyone's going to now bid $100. They're going to bid $20.50 or $19.25 or some such. If the last sale was for $20 and your broker really came to the floor and offered to buy for $100, I suppose someone would sell to him very quickly before he realized what an outrageous price this was.
I use TD Ameritrade, and on their web site, if I give a price limit on a buy that's more than a small percentage above the last sale, they reject it as an error. I forget the exact number but they won't even accept a bid of $80 if the stock is going for $40. They might accept $41 or $42, something like that.