There are two main ways to get exposure to other currencies: you can buy them in the open market (FOREX), or you can buy instruments (such as ETFs) which reflect the currencies’ cross rates.
For example, FXE reflects the rate of exchange between the US dollar and the Euro. It is trading in units of exchange rate times 100 (for example, if today, FXE is trading at $130, it means that the rate of exchange is $/Euro = $1.30).
There are many other exchange-traded funds, which reflect inter-currency rates of exchange or the entire baskets of currencies. There are more complicated instruments, which even take advantage of the interest rates in various currencies, such as DBV – “PowerShares DB G10 Currency Harvest.” Some ETFs will offer positions in international companies while also hedging against currency fluctuations.