Mail from Honduras takes a week to 10 days to reach the United States. Letters and postcards make it just fine if posted from Tegucigalpa, San Pedro Sula, La Ceiba, or Roatán, and if they don't look like they contain anything of value. You'll pay L12 for a card or a letter up to 20 grams.
For timely delivery or valuable parcels, use FedEx, DHL, or UPS, which have offices in Tegucigalpa, San Pedro Sula, and La Ceiba. Because of the limited number of international flights, overnight service is usually not available. Plan on so-called next-day delivery, really taking three to four business days from Honduras.