I believe a certain country's currency will fall sharply (compared to the USD) in the next couple of years. Is it possible for me to profit off of this situation? If so, how?
You either short that currency against the USD or you buy the USD against that currency. Both are the same thing and will give you the same result.
But be careful as the FX market is open 24 hours (except Sundays), so make sure you apply risk management unless you plan to be stuck to your screen all day and night.
If you don't want to do FX trading, then you can just buy some USD notes and wait for the other currency to fall before you exchange back to the other currency.
You borrow that currency and immediately exchange it for USD. Then you hold the USD (as collateral for the money you borrowed). When/if the currency falls sharply, you buy it back using some of the USD. Since you no longer have a loan, you can then withdraw the USD. You can do this with pretty much any forex broker.
Note that you will have to pay interest on the loan but will get interest on the USD. Likely the USD interest rate is lower, so you will have a net cost. Also note that if the rate moves against you for too long, you will need to add more USD to keep the loan properly collateralized. You could face one or more margin calls if it takes too long for the currency to drop.
This is a very risky thing to do.