In tourist areas of most countries, you'll manage fine. Pharmacists tend to be well-educated, many studied from English-language materials, and pharmacies in tourist zones, international hospitals, and upscale malls often deliberately staff English speakers. Big chains in tourist-heavy countries are generally your best bet; a small neighborhood pharmacy in a residential district is where language gets thinner.
Labels are the weaker link. Packaging and instructions are usually in the local language only, though the pharmacist can write dosage instructions for you, and many medicines list the active ingredient in Latin script somewhere on the box, which is the real key.
That last point is the tip that solves most problems: know the generic name of what you need, not your home brand name. Brand names change across borders, but asking for the active ingredient works everywhere, and showing it written down or on your phone bridges any language gap. Translation apps with camera mode also read labels convincingly now.