Tegucigalpa is the capital of Honduras.
North towards Comayagua/San Pedro Sula/Tela
The highway leaving Tegus for the north is a place called El Carrizal. You can take one of the rapidito buses from the main park for 11 Lempiras. The rapidito says "El Carrizal" on the front, and you just take it all the way to the end. There's an Uno gas station where you can ask for a ride or just thumb it at one of the bus bays. It is a 20 minutes walk from the bus up to the gas station.
South towards El Salvador/San Lorenzo/Choluteca
The highway to the south leaves the city from the last bus stop of the bus going to Louarque. They cost about half a dollar from the central square. After getting out just follow the road for 200 meters and you will see a gas station. Asking there or thumbing right next to it usually works fine.