I understand there are multiple sources for stocks or FX market prices, but what leaves me completely puzzled, is how can short term traders (speculators really) make their decisions based on price data from sources other than their broker; especially for forex. If one is tracking a particular currency pair with broker A, but data comes from source B, then they can't be sure that is the price they're going to get, right?
This is a complicated subject, because professional traders don't rely on brokers for stock quotes. They have access to market data using Level II terminals, which show them all of the prices (buy and sell) for a given stock.
Every publicly traded stock (at least in the U.S.) relies on firms called "market makers". Market makers are the ones who ultimately actually buy and sell the shares of companies, making their money on the difference between what they bought the stock at and what they can sell it for. Sometimes those margins can be in hundreds of a cent per share, but if you trade enough shares...well, it adds up.
The most widely traded stocks (Apple, Microsoft, BP, etc) may have hundreds of market makers who are willing to handle share trades. Each market maker sets their own price on what they'll pay (the "bid") to buy someone's stock who wants to sell and what they'll sell (the "ask") that share for to someone who wants to buy it.
When a market maker wants to be competitive, he may price his bid/ask pretty aggressively, because automated trading systems are designed to seek out the best bid/ask prices for their trade executions. As such, you might get a huge chunk of market makers in a popular stock to all set their prices almost identically to one another. Other market makers who aren't as enthusiastic will set less competitive prices, so they don't get much (maybe no) business. In any case, what you see when you pull up a stock quote is called the "best bid/ask" price. In other words, you're seeing the highest price a market maker will pay to buy that stock, and the lowest price that a market maker will sell that stock. You may get a best bid from one market maker and a best ask from a different one. In any case, consumers must be given best bid/ask prices.
Market makers actually control the prices of shares. They can see what's out there in terms of what people want to buy or sell, and they modify their prices accordingly. If they see a bunch of sell orders coming into the system, they'll start dropping prices, and if people are in a buying mood then they'll raise prices.
Market makers can actually ignore requests for trades (whether buy or sell) if they choose to, and sometimes they do, which is why a limit order (a request to buy/sell a stock at a specific price, regardless of its current actual price) that someone places may go unfilled and die at the end of the trading session. No market maker is willing to fill the order.
Nowadays, these systems are largely automated, so they operate according to complex rules defined by their owners. Very few trades actually involve human intervention, because people can't digest the information at a fast enough pace to keep up with automated platforms.
So that's the basics of how share prices work. I hope this answered your question without being too confusing!
To add a bit to Daniel Anderson's great answer, if you want to 'peek' at what a the set of bid and ask spreads looks like, the otc market page could be interesting (NOTE: I'm NOT recommending that you trade Over The Counter. Many of these stocks are amusingly scary): http://www.otcmarkets.com/stock/ACBFF/quote
You can see market makers essentially offering to buy or sell blocks of stock at a variety of prices.