Here's a breakdown of your options:

By Air
-Adolfo Suárez Madrid-Barajas Airport (MAD): This is the main international airport serving Madrid, located about 13km northeast of the city center. It offers numerous connections to destinations worldwide.

By Train
-Puerta de Atocha Station: This is the largest railway station in Madrid, with high-speed connections (AVE) to major Spanish and European cities.
-Chamartín Station: Another major train station, offering national and international connections, particularly to the north of Spain.

By Road
-Extensive Road Network: Madrid is well-connected to the rest of Spain and Europe via a network of motorways (autopistas) and highways. 

Once you arrive in Madrid:
The city offers an excellent public transport system, including a metro, buses, and taxis, making it easy to get around. You can also find ride-sharing services and bike rentals.