Under US federal law, "registration or voting notices, forms, instructions, assistance, or other materials or information relating to the electoral process, including ballots" must be "in the language(s) of the applicable minority group(s), as well as in English."
If census data show one of the items below, then the voting materials must be in that language.
• more than 5 percent of the citizens of voting age of the State or political subdivision are members of a single language minority and are limited-English proficient;
• more than 10,000 of the citizens of voting age of the political subdivision are members of a single language minority and are limited-English proficient; or
• in the case of a political subdivision that contains all or any part of an Indian
reservation, more than 5 percent of the American Indian or Alaska Native citizens of voting age within the Indian reservation are members of a single language minority and are limited-English proficient.
You don't necessarily have to provide alternate languages everywhere in a particular state. It is also by "political subdivision," which is usually a county. So County A may print ballots in English & Spanish, while County B prints them in English and Mandarin. However, if an entire state is deemed to be covered, then all ballots in that state must be in the alternate language. In California, for instance, all counties must provide Spanish language ballots; some counties must add other languages.
States may have additional requirements.