How does the stock price determines

It's all about supply and demand.

 For those of you who are actually curious about the exact mechanics, the open price is calculated by the stock exchange like the NYSE (the New York Stock Exchange) for example, or NASDAQ. (National Association of Securities Dealers Automated Quotations)

• NYSE is an auction market that uses specialists or designated market makers
• Nasdaq is a dealer market with many market makers in competition with one another. 

Dealer vs. Auction Market

• Dealer market: Market participants do not buy and sell to one another directly. Transactions go through a dealer which, in the case of the Nasdaq, is a market maker. More than 260 market-making firms provide liquidity for Nasdaq-listed stocks. This competition helps ensure buyers and sellers are getting the best prices.
• Auction Market: Before the market's official opening time, market participants can enter buy and sell orders starting normally at 3 hours prior to the official opening. These orders are matched, with the highest bidding price paired with the lowest asking price. At the NYSE, the job of maintaining markets falls to designated market makers (DMMs), formerly known as specialists. The DMM is the human point of contact for the listed company on the NYSE trading floor. DMMs provide stability by taking the other side of the trade when imbalances occur, buying when investors are selling, and vice-versa. They run the opening and closing auctions, using human input and algorithms to help promote price discovery when the volume is typically at its highest. According to the NYSE, DMMs provide a big amount of liquidity. (approximately 20%)



Automated pricing based on supply and demand. bid and ask:

• When you place an order to buy a share at a certain price that is called your “bid” and when you place an order to sell your shares at a certain price that’s called your “ask”.

• Every morning stock exchanges set the opening price by taking pre-opening orders and offers.
• The stock price is the highest amount someone is willing to pay for the stock, or the lowest amount that it can be bought for.
• The calculation of prices is completely automated, software-driven, and anonymous at the specific exchange, and the price is calculated by electronically matching bids and offers for a particular share recorded in an electronic limit order book (ELOB).
• The ELOB contains all the bids – asks for a particular share and the system matches the best bids and asks to execute an order. The price at which a transaction is executed is called the last traded price (LTP) and that’s what you see on TV screens. It’s usually the price that results in most stocks being sold.

Some people say we should add the dump and pump etc to the above, but at the end of the day these are part of supply and demand in larger scale.