By bus
The bus terminal is about 2 km northeast of the center, take one of the trucks waiting in front of the terminal - which serve as local buses 3.5 cord - to the center, or take a taxi for about C$20.
From Managua : Take the vans leaving from Mercado Israel Lewites or the microbuses camionetas leaving from UCA Universidad Centro Americana. The vans from Mercado Israel Lewites are fiteen-passenger vans that are fairly crowded, but not excessively uncomfortable, particularly when one sits next to a window. Buses run regularly, leaving from the Mercado every 15-20 minutes. Buses leave from La UCA beginning at 4:30am until approx. 9pm. They leave whenever they are full, usually every 15 minutes. The bus from either terminal costs C$ 46. If you take the bus, make sure to get an expreso - otherwise the bus makes stops to pick up passengers on the side of the road along the way.
From Esteli : There's one direct bus daily. If you miss it, you've got to change in San Isidro on the Panamerican Hwy.
From Matagalpa : There are 2 direct busses running daily, otherwise take a bus to San Isidro and transfer to Leon.
Direct transportation is also available directly from the Managua airport via private van service.
By car
Just about anyone in Managua can tell you how. The Carretera Vieja to León old road to León is in the worst shape it has been, ever. It is littered with potholes and takes a round about way to Leon. The Carretera Nueva is in great shape I hear). It's about 90 kilometers from Managua to León, about a 90 minute trip depending on how fast you drive. Stop for quesillo and tiste in Nagarote or La Paz Centro, the two towns the Carretera Nueva goes through on the way. You will find the turnoff to the Carretera Nueva a León at KM 6 1/2 on the Carretera Sur.
If you are coming from the north Esteli on the carretera norte, take the turn north of Matagalpa, at San Isidro I think, and save yourself the trouble of going through Managua. This highway was just recently repaired and is in great shape. It takes about 2 hours by bus to get to Leon from Esteli or Matagalpa.
By plane
Nearest commercial airport is in Managua. Managua is roughly an hour and a half drive from León.