What determines a stock price?

I'm confused. I have read that it is what people are willing to pay for it. I have also read that it is a share of the company's value. So if a stock is worth $10, and people are willing to py 11$, how do I know what part of the stock I'm paying for is actual ownership in the company. What are these terms called? Is it P/E Ration? Please help.
Additional Details
I mean, how do I know what part of the stock is actual ownership in a company VS the extra I paid to buy the stock because of demand (because other people are willing to pay more.)

A stock prices reflects supply and demand. There is a bid and ask price. A bid is what someone is willing to pay for it and ask is what someones willing to sell it for. When you see the ticker on CNBC or something, that's what the stock just exchanged at. Using limit orders, you can specify how much you buy or sell a security for. If you place a market order, you will get the lowest ask price in line. And visa versa. The specialist's job to provide a fair and orderly market and match buyers and sellers.

The P/E Ratio is the Price to Earning Ratio. Its a valuation ratio of a company's current share price compared to its per-share earnings.

Market Value per Share/EPS

Here's a good explanation of P/E.
http://www.investopedia.com/terms/p/price-earningsratio.asp

Instead of asking the questions of these type, it is always better to talk to the Expert of this field for your better understanding and accuracy of the answers

The price is set by the specialist who handles the stock on the NYSE. What you pay for it is called the spread. The seller makes the $$. The value is determined by the float. How many shares are out there and what is the value of the company and then they look at the pe ratio. So the bid and ask are entered into SOS every time a share is traded and the specialist has just a couple of minutes to set the new spread. If not he can and will be fined by the NASD and or the NYSE.
I am a former registered principal.

Like everything else, it is supply and demand. P/E means the ratio of the price to its earnings. That is not a bad way to evaluate the value of a stock, but not everybody pays attention to it. Some people look to the future and are willing to pay a lot now for small earnings now but are gambling that the company will have higher earnings in the future. Some people believe a company's stock value will climb because it will be bought out. As of 15 or 20 years ago, a price / earnings ratio of 10 to 1 was considered necessary for a stock to be a good buy, but that rule is seldom followed now.

There is another thing to look up. It is called book value. But there is a lot to be said for the Price/Earnings ratio for valuation. For instance, J. C. Penney announced today about lower earnings in a quarterly report. The price as I last checked was $83.57, down $2.78. The P/E now is 17.88 according to the Wall Street Journal. Poor earnings brought the price down because part of the price was pegged to the earnings. The WSJ's valuation chart still had last year's figures, so I'll go from there: the P/Book at the end of last October was 4.88, down from 5.02 this time last year. That means you go to the stockholder equity on their balance sheet, divide by the 224-ish million shares outstanding, then compare that to the price for the stock at that time. The price fell or the equity fell, or both. So you are buying the stock at about $4-5 premium, per dollar of equity. When you buy the stock today, you buy it at a $17.88 premium for every dollar of profit (earnings) the company makes. But if it is going to make more profits in the future, then it is possibly a good buy. Yet if it won't, then you expect the price to fall. Another thing sometimes happens, the price doesn't fall as fast as earnings, in expectation. If that is the case, the P/E will rise whether the stock falls or not. That is a still bigger premium you are paying for the priviledge of owning a piece of a retail store chain. Interestingly, JCP is running at about 86% of the industry average P/E, and 143% of the industry P/Book. That tells me that there is room for it to fall more, but there are a pile of others who should have fallen more than Penneys. In that way, you can scout the competitors because there are more equitable and profitable companies out there (of course, you will have to do some digging because there are a pile of them in retail stores that are worse). At least now you have a couple of yardsticks to eliminate those with comparatively inferior valuations.

For your additional notes. People for various reasons want to buy the stock and other people for equally diverse reasons want to sell it. Some orders are for the market, but some are for specific prices, or the market if it hits one of those specified prices. There usually is a backlog of orders, some offering, some bidding and when they match, there is a sale. When they don't match, there is a spread (between bid and asked). At some point someone will place a market order to buy, so they just bought the stock at whatever the lowest asking price was. At some point someone will place a market order to sell, so they just bought the price at whatever the highest bid order was. Meanwhile, people interested will pick up sides and place more orders, often somewhere in between so they won't have to have their order queued behind those stalled because of the spread, which I've done myself. The bid was $x.02 and asking was $x.10, so I modified (changed) my bid order to $x.04. At some point someone snapped it up, but since all the other buy orders were still at $x.02 and all the other askings were still at $x.10, things once more sat until someone budged. Now if there is a lot of good news and people are buying plus some bad news and people are selling, then that is when it gets exciting and the price flops all over the place.

A stock is a percentage ownership in a company. So the stock price times the number of stock the company has will tell you the company's total value. If that is determined through the market then yes it is what people are willing to pay for it(or sell it for that matter). P/E ratio is price to earnings.

You starred your own question twice? The price is the price, bid is what people want to pay, ask is what people want to sell at, thats that. I don't know where to find the "worth" isn't that what the stock is valued at?

The public's perception of the value of a company.

supply and demand
also, a company has a market value, based on earnings

Stock price depends on the financial performance of the company, Nature and scope for the particular industry, good management team, stability in profits, Expectation of increased profits in the forthcoming year, Asset Liability Ratio, Political climate over the particular industry, Company's ability to bear lossesetc. Eventhough if you invest in a ompany after analysing these factors, isome people will call its still more or less a gambling only.

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