Dental emergencies abroad are less scary than people fear, because good private dental care exists in nearly every sizable city and several countries are actually dental tourism destinations precisely because quality is high and prices are reasonable. For finding an English-speaking dentist quickly, three routes work almost everywhere: your embassy's website usually lists English-speaking medical and dental providers, your hotel or local expat groups can name the clinics foreigners actually use, and international clinics in big cities almost always have dental departments or referrals.
On costs, honesty requires saying they vary too much by country to quote: the same root canal can be a minor expense in parts of Asia or Eastern Europe and a major one in North America. Private clinics will give you a written estimate before treatment if you ask, which is standard practice and worth insisting on. Note that many travel insurance policies cover only emergency pain relief, not crowns or ongoing work, so read your policy before agreeing to a full treatment plan.
For genuine emergencies like knocked-out teeth or severe swelling with fever, treat it as medical and go to a hospital, since infections in the jaw can turn serious quickly.