What should you write in a letter to your host family?
Let me assume you mean before you meet the family (since after your stay you will have a good relationship with them.) A host family has some motives for offering their home to a stranger from another culture. You might begin by thanking them in a courteous way for doing so, then offer a sentence about why you have requested a host family experience. In the body of the letter, express your enthusiasm for learning more about their culture, and express the wish and hope that you will represent your culture in a positive way. (You might end this part of your letter by expressing your admiration for the program itself.) The second section of your letter can address practical matters and some preferences you might have—“My English (or whatever language is native to your host) is (and describe your level of bilingualism)”; “I am very tall” (or any other physical feature you might need them to know about—allergies, etc.); you might also here give them some idea of your “comfort” with their culture, your familiarity with it, your previous exposure to it (perhaps by media exposure), etc. Then in a new paragraph, ask them (rhetorically) what you can offer them—would they like to learn your language? your culture’s culinary habits? your country’s music? etc. and suggest that might be a good subject for an early discussion once you arrive. Be courteous in your rhetoric, but not subservient or “beneath” them (and avoid all political comments). Express your excitement and anticipated enjoyment (parenthesizing that your education is really the primary purpose for this experience.) Close with a friendly salutation (perhaps one unique to your culture, with translation into their culture’s equivalent). The real purpose of this letter is to begin the connection, not to display your qualities except indirectly, so the primary rule is to present yourself as an open mind, without preconceived notions of right and wrong cultural behaviors.