Google is indeed your friend, and the fact that you are from US, an English-speaking country, is a great plus.
Now let me say. When visiting other countries, you must check with your doctor and local regulations because not all drugs can be sold by a random stranger walking into pharmacy. You may need an internationalized prescription, which is handled by the pharmacist
The key is finding the generic name of the drug, which often matches the active ingredient(s)' name, with the help either of the package or online. Secondarily, you will have to deal with the dose.
Suppose you have a prescription for... random... Solurex.
1. Find the active ingredient, in English
A quick search for [pharmaceutical name] generic name reveals that Solurex is based on something called Dexamethasone.
You just achieved 98% of your job!!. Now you just have to pick the correct local drug.
2. Translate the name into any language
With the help of an online translator?
- Spanish: Dexamethasona
- Norwegian: Deskametason
- Russian: Дексаметазон
- Hebrew: דקסמתזון
- Simplified Chinese: 地塞米松
Of course, if your pharmacist speaks English they can understand what medication to serve you. Remember that the pharmacist wants to know both the active ingredient(s) and its dose. I helped on finding the ingredient name.
Most if not all pharmaceutical products are equivalent to their generic drug despite a different commercial name. So you can buy just any Dexamethasone anywhere even if it's sold under different names, as soon as the dose matches your prescription.
Don't expect any drug to be available easily. Jurisdictions vary, certain drugs couldn't be authorized at all in the target market. Simple everyday products like Aspirin (which is the commercial name), paracethamol (which is the generic name that you can find e.g. as Beechams Flu Plus Hot Lemon) are of course widely available and mostly require no prescriptions. For more specific medications, e.g. anti-cancer, anti-diabetes, life-saver, you may have to buy home and carry with you. Indeed, this is the safest way.
As a last resort you could always try finding a local doctor to give you a prescription but that could prove difficult or expensive depending on your destination.