Most nationalities don't need a visa, and entry and exit is easy if you follow the rules.
Customs checks are pretty lax; while police and customs officers are entitled to search you at any time, especially in border areas, they rarely do. Even searches at the airport tend to be perfunctory, though you have to submit your luggage to an x-ray upon entering and exiting Honduras. The exception is if something about your appearance or demeanor suggests to the officer you may be carrying drugs.
Beyond drugs, travelers are not allowed to remove any ancient artifact or endangered animal or plant, whether live or a product made from these. It’s smart to keep receipts for any item you buy, and especially for anything that might be confused for being a restricted product, such as an especially good Maya replica.
Most travelers do not require visas to enter Honduras, and simply receive 90-day tourist cards on arrival.
Citizens of the EU, Australia, Canada, Japan, New Zealand and the USA normally receive free, 90-day tourist cards when entering the country. This also applies to nationals of the countries signed up to the CA-4 border agreement – Guatemala, Nicaragua, Honduras and El Salvador.
Other nationalities, including most Asian and African countries, have to apply for a visa in advance from a Honduran embassy, and pay a fee of US$30.
Once inside Honduras you can apply for a one-time 30-day extension (US$20) at the main immigration office in Tegucigalpa (travelers have reported problems gaining extensions in other offices). Or just take a trip outside the CA-4 border agreement area (Belize and Costa Rica are nearest) for at least three days, then get a new 90-day visa upon re-entering Honduras.