There are several ways to get from Madrid airport to the city center. Here are some of the most common options:

1. By Metro: Madrid's metro system is efficient and affordable. You can take Line 8 (pink line) from any airport terminals to Nuevos Ministerios station, which is in the city center. The journey takes around 30-40 minutes and costs €4.50. You can buy a single ticket or a 10-trip card ("Metrobús").

2. By Bus: Several bus routes operate between the airport and the city center. The most popular is the Exprés Aeropuerto, which runs 24 hours a day and takes around 30 minutes to reach the city center. The fare is €5.00. Other bus routes include the 101 and 200. You can buy tickets at the airport or on board the bus.

3. By Taxi: Taxis are available 24 hours a day at the airport. The journey to the city center takes around 20-30 minutes, depending on traffic. The fare is typically around €30-€35. Make sure to only take licensed taxis with a distinctive white color and a red stripe.

4. By Private Transfer: You can also arrange a private transfer from the airport to your hotel or destination in the city center. This is a convenient option if you have a lot of luggage or want a more comfortable and personalized service. Prices vary depending on the company and type of vehicle.

The cost of a private transfer from Madrid airport to the city center can vary depending on the company, the type of vehicle, and the distance to your final destination. However, as a rough estimate, you can expect to pay around €40-€60 for a standard sedan or €60-€80 for a minivan or larger vehicle. It's always a good idea to check with a few different companies and compare prices and services before booking. Some companies may also offer fixed rates for specific routes or destinations, so it's worth asking about any discounts or special offers that may be available.

The time it takes to travel from Madrid airport to the city center depends on the mode of transportation you choose and the traffic conditions at the time of your journey. Here are some approximate times for the different options:

1. Metro: The metro ride from Madrid airport to the city center takes around 30-40 minutes, depending on the specific location of your destination and any transfers you may need to make.

2. Bus: The express bus (Exprés Aeropuerto) from Madrid airport to the city center takes around 30 minutes, depending on traffic. Other bus routes may take longer.

3. Taxi: A taxi ride from Madrid airport to the city center takes around 20-30 minutes, depending on traffic and the specific location of your destination.

4. Private transfer: The time it takes for a private transfer from Madrid airport to the city center can vary depending on the specific location of your destination and traffic conditions. However, it usually takes between 20 and 40 minutes.

It's always a good idea to allow extra time for unexpected delays, especially during rush hour or in heavy traffic.