Getting there in Honduras:

By Plane:
Ramón Villeda Morales International Airport (SAP) is the busiest airport in Honduras, slightly busier even than Toncontín International Airport near the capital Tegucigalpa, with around 600,000 passengers a year. It offers a wide range of domestic and international connections, including to most countries in Central America and cities in the USA like New York City, Atlanta, Miami and Houston.
Toncontín International Airport (TGU) near Tegucigalpa has several airlines with international connections including TACA to and from Miami, San Salvador and Guatemala City. Several airlines have flights to Belize and Nicaragua and other destinations include Panama City and Houston.
Juan Manuel Gálvez International Airport (IATA: RTB, ICAO:MHRO) is also known as the Roatan International Airport. This airport has regular service to La Ceiba, San Pedro Sula, Tegucigalpa, Belize City, San Salvador, Miami, Houston and Atlanta. There is also seasonal service to Toronto, Montreal, Ottawa and Newark. There are direct flights with Blue Panorama Airlines to/from Milan.
Golosón International Airport (LCE) near La Ceiba offers a few international connections as well, like those to and from Montreal and Grand Cayman, Cayman Islands.

By Train:
For the time being, there are no rail options between Honduras and neighbouring countries.

By Car:
Honduras is connected to El Salvador and Nicaragua via the Pan-American Highway and and to Guatemala on the Western Highway, but most foreigners don't travel by car. If you do, be sure to arrange everything before arriving on the border, stay alert and avoid travelling when it's dark, as borders might be closed or dangerous areas

By Bus:
The main crossings to Guatemala are Agua Caliente, El Corinto and El Florido. Crossings to and from El Salvador are at El Amatillo and El Poy and to Nicaragua at El Espino, Guasaule and Las Manos. There are frequent buses to these border posts, but just a few buses travel directly between Tegucigalpa and neighbouring countries/capitals.

So most of the time you just cross the border on foot and take an onward bus on the other side. Try Ticabus for direct international services.

By Boat:
There are several connections from towns in the south of Belize like Dangriga and Punta Gorda to Puerto Cortes in Honduras, but usually only once a week. There's also a boat from Lívingston and/or Puerto Barrios in Guatemala to Omoa in Honduras, usually at least several times a week. You might find boats to Nicaragua on the Caribbean coast and to both Nicaragua and El Salvador on the Pacific side, but services are infrequent and not timetabled.

To Belize (Big Creek & Placencia), Departure: Puerto Cortez - Every Monday at 11:30am (Leaves from "Puente Laguna" (Lagoon Bridge) next to Delfin Restaurant in Puerto Cortes)
To Honduras (Puerto Cortez), Departure: Placencia - Every Friday at 9:30am (Leaves from Placencia Shell Dock), Departure: Big Creek - Every Friday at 11:00am.