The mechanics of a trade are virtually identical to those in other markets. The only difference is that you're buying one currency and selling another at the same time. That's why currencies are quoted in pairs, like EUR/USD or USD/JPY. The exchange rate represents the purchase price between the two currencies.
Example: the EUR/USD rate represents the number of USD one EUR can buy.
If you think the Euro will increase in value against the US Dollar, you buy Euros with US Dollars. If the exchange rate rises, you sell the Euros back, and you cash in your profit. Please keep in mind that forex trading involves a high risk of loss.