Start with structure: find out how the local system works, because in some countries you register with a general practitioner who refers you onward, while in others you book specialists directly. Getting into the system early, before you are sick, is the single best move a newcomer can make.
For finding someone trustworthy, personal recommendations still beat everything. Ask colleagues, neighbours, and local expat groups, where questions about English-speaking doctors are among the most common posts and the answers are usually well tested. Embassies often maintain lists of doctors who speak your language, and international clinics in major cities cater specifically to foreigners, though at higher prices than local providers.
Verify the basics: proper licensing, hospital affiliation for specialists, and whether they accept your insurance, since payment models range from public coverage to cash-up-front. Bring your medical history and a list of current medications, ideally translated, to the first visit. And keep a note of how emergency care works where you live, including the emergency number and nearest hospital, because that is not information you want to be researching mid-crisis.