Honduras is not a party to the Hague Service Convention and has no service treaty with the United States. Formal service is by Letters Rogatory through diplomatic channels, which typically take a year or more. In practice, most U.S. litigants serve defendants in Honduras through a local agent or lawyer, where local law doesn't prohibit it and the court accepts it.
Spanish is the language of the courts. Honduras is a party to the Inter-American Convention on Letters Rogatory, but not in a form that creates a treaty relationship with the United States, so that route isn't available to U.S. litigants. Honduras is a party to the Apostille Convention, so U.S. documents that need to be used there can be authenticated with an apostille.