In the forex market, hedging means ensuring you are prepared and have measures in place in case the market goes against you. Diversification is a common approach to hedging. You can diversify your portfolio by including assets that are weakly correlated with one another. For example, USDJPY and USDCHF currently have a daily correlation of 92% which is high, and thus buying them together won’t help you hedging. However, USDJPY and AUDUSD have a negative daily correlation of -0.7%. Thus, if you buy USDJPY you can hedge your position by buying AUDUSD as well (since they are negatively correlated rate and move in opposite directions). However, buying USDJPY and USDCHF at the same time will expose your portfolio to extra risk since they are correlated.
Another similar approach is to simply open a position in the opposite direction to the one you have. For example, if you had sold EURNZD but it went up, then you buy the EURNZD without closing the first position. This way, you temporarily fix your losses from the first position until you close any of the two positions. This approach is effective in that you may win on either one of the two positions, and that it gives you some time to gather more information.
There are other ways to hedge your positions, such as by using options. If you have bought the Euro against the USD (EURUSD), for example, you can buy a put option to reduce your downside risk (i.e. the risk of loss in case the exchange rate drops). If you have sold the pair, you can hedge your position by buying a call option (to cover the risk of an increase in price). The disadvantage of hedging with options is that those contracts have an expiration date, and thus they only provide temporary protection at best. Moreover, the prices of the options contracts often increase if the risk is high, and thus the cost of protection increases.
Other hedging tools include buying (or selling) futures contracts. With futures contracts, you agree to buy (or sell) something at a specific price at a specific point in the future. For example, a producer of oil agrees to sell 1000 barrels of oil to a customer in three months from now at $40 per barrel, although the price is $45 now. The oil producer is hedging against an expected steep decline in the price of oil (to below $40 per barrel). Futures contracts are usually used by non-speculative traders such as buyers and sellers of physical commodities, among others.
Companies can also make use of other hedging options such as credit default swaps or interest rate swaps, among others.