Usually, when people talk about Forex they refer to the spot market. In the spot market currencies are traded physically or electronically “on the spot” at the current market price.
For an average person, the most practical way to trade Forex is via an online broker. Brokers pair all buy and sell orders and re-sell or hedge the remaining part to other brokers and/or financial institutions. The prices quoted by the broker are usually aggregated from multiple sources and might slightly differ between brokers.
It is also possible to trade currencies via Futures, Options and Exchange-Traded Funds (ETFs) but those markets are out of the scope of this e-book.
When you place a trade in Forex, you are always long or short one side of the pair against the other side of that pair. Therefore, you are always long and short at the same time.
When you buy the EUR/USD pair that means that you simultaneously buy the Euro and sell the USD. When you short the Euro, you sell the Euro and buy the USD.