By ship
There's a boat running twice a week from San Carlos via Ometepe to Granada and back. It leaves San Carlos at Tuesday and Friday at 2 pm.
By train
The old train that once existed was shut down during the era of Violeta Chamorro. So, no, there's no possibility to take any train to get there. Nevertheless, you can have the chance to visit the old train station, which is used as a technical school sponsored by the Spanish Cooperation.
By bus
Buses are available from Managua on a quarter-hour basis from 5AM to 10PM US$1. Granada is easily reached by first-class buses from neighboring Costa Rica and Honduras.
By plane
Fly to Managua the capital of Nicaragua and from there make your way by bus every half hour from Mercado Huembes or the La UCA station or taxi around $35 from the airport depending on your bargaining skills. As an alternative, you can take an air con shuttle for $15 from the airport to Granada. In most cases, the shuttle will deliver you to any point in Granada. There is a tourist information counter as soon as you clear immigration. Ask the representative and she´ll point you to a reputable shuttle service. The trip by taxi or shuttle is about 40 minutes. Another option may be to fly to the Liberia Airport over the border in Costa Rica, but it would involve about 5 hours of travel and a border crossing. Rental cars are not allowed to cross the border, but agencies will arrange for car swaps and pickups on the other side of the border. Managua is by far your best option.
There is a small airport a few miles from Granada on the highway to Masaya. The airport was served only by Nature Air, which offered flights from San Jose and Liberia, Costa Rica, the flights are now going into Managua International airport. Flights originate in San Jose, Costa Rica's capital and also from Liberia "LIR" in Guanacaste Costa Rica.
By car
Yes you can get there by rental car, which is often really expensive to hire, since imported cars are expensive too and the risk of theft is high. Most of the principal highways are in good condition, however potholes and other obstacles can surprise you, so be alert. Secondary roads range from ok to horrendous. The roads from the airport are good, then rather bad, then good - on the most direct route.
From Costa Rica, take the Panamerican Highway, which leads from San José through Liberia, the border crossing at Penas Blancas, first bigger town in Nicaragua is Rivas, after Nandaime take a right onto the Granada-Nandaime road. Look for Granada-related signs.