The options available to you depend in part on whether you yourself are physically abroad or have plans to be.
For example, if you moved to say...Japan to teach English for a year, you could establish residency (not necessarily long-term residency, but residency based on having a working visa sponsored by the Japanese company that hires you).
You would walk to a bank, show them your Japanese home address and residence card, and open a local Japanese bank account. Get paid in yen, convert and deposit any additional money of your own, and voila, your money is abroad in a different currency. If/when you leave Japan, your account and money can stay there at low or no annual fees.
Another option is to visit a "country"/jurisdiction such as Hong Kong, whose banks welcome non-resident account holders. Open a personal bank account, convert and deposit your money in HKD and you're set.
There are other ways, but the above examples stick to what is simple and familiar to most people: personal bank accounts.
Important: If your home country happens to be the U.S., you will need to report these accounts to Uncle Sam every year in an FBAR and (maybe) FATCA report.