There is a bus going to Madrid from Aranjuez every half hour or so. It leaves from near the "Isabel II" gardens, in the center of town. Costs about 3 euros I thinks and takes about 30-40 minutes.
In Madrid it leaves from Mendez Alvaro bus station.
As it is inside Madrid's Community, you can get here with a "Cercanias" train from Atocha station. Take the line C3.
It costs 2.65 euros each way and you can buy return tickets too. It takes 30 minutes. There are trains every half an hour.
When you arrive to the station, turn right, then left and in 10 minutes you will arrive to the Royal Palace.
If you are in a hurry or don't wanna walk much, you can see all Aranjuez in an hour with this little train, that costs 5 euros.
It goes all around the town, departing from the right side of the Palace's entrance (look for a little green kiosk).
I think that the best way to visit Aranjuez from Madrid is by train. It takes about 40 minutes.
- In Madrid, trains leave from Atocha-Puerta de Atocha station (Glorieta del Emperador Carlos V, also known as Glorieta or Plaza de Atocha. Metro: Atocha Renfe (line 1).
- In Aranjuez, the station is just 10 minutes walking from the Royal Palace (Calle de la Estación). There are buses you can take if you don't want to walk.
From Madrid, road A-4.
Road distances to Aranjuez from:
- Madrid: 49 kms.
- Málaga: 486 kms.
- Rome (Italy): 2.008 kms.
- Athens (Greece): 2.639 kms.
Checking the web, you can find more road distances together with the driving times and the best routes.
From Madrid you can take the train to Aranjuez. You must go 30 min. From Atocha go a train every 30 min. And the ticket is not expensive - about 5 Euro.
These were the old vessels to go through the Tajo river in the old times. They don't run anymore now, but you can see some here and there...