If I want to buy something from England, I have to pay for it with British pounds. To get the pounds, I have to purchase them with my U.S. dollars. There is (are) market(s) for currency, per se, i.e. where various currencies are bought and sold for other various currencies. The price is set as in any other market, e.g. commodities markets. If a gov’t. or central bank feels that it needs to adjust the value of its currency vis-à-vis other currencies, it enters the market and buys its own currency with foreign currency it keeps on hand, or it sells its currency in exchange for foreign currency.
Suppose that the British central bank felt that the £ was too cheap. It could pull a sizeable sum of money in the form of Japanese yen (¥) out of its coffers and use the ¥ to purchase £ in the money market. This jump in demand for £ will drive up the price of £ across the board because everyone seeking to purchase £ will be competiting with the new buyer in the market, the British central bank.
Whether it succeeds or fails depends on how much currency a central bank has. If it has insufficient foreign currency to keep the price of its currency up, then it runs out of foreign currency and the price of its own currency then drops. OTOH, if the central bank wishes to keep the price down, it has to sell its own currency in exchange for foreign currency. If it runs out of its reserves of domestic currency, then the price will rise as the market determines.
Suppose that you are a national gov’t. and you are getting pressure from your beef exporters because your currency is too high. That is, to buy your cattle herders’ beef foreigners need to purchase your currency in exchange for their own, and then use your currency to purchase beef from your producers. If the cost of your currency is high for some reason, they’ll buy less of it and therefore buy less of your producers’ beef as well. You may respond to this political pressure by selling large amounts of your own currency in the currency market and, you hope, drive down the price of your currency. If you are successful, then your beef exporters will export more beef.