From Cologne:

(e.g. from the Airport Cologne/Bonn)

A4 in the direction of Aachen

• to the motorway intersection Aachen
• there remain on the A4 (get into the right lane) in the direction: Antwerp, Eindhoven, Heerlen, Aachen
• exit no. 2: leave the motorway at Aachen Laurensberg
• drive in the direction of Aachen - …
  
  ... Remain on this road until after the place name sign Aachen
• behind that turn right (in the direction of Laurensberg)
• and continue to drive straight (to the Schloß-Rahe-Straße)
• turn right and follow the sign “Schloß Rahe”
• drive through the railway embankment tunnel.

From Düsseldorf:

(e.g. from the Airport Düsseldorf):

A44 in the direction of Aachen

• to the motorway intersection Aachen
• there keep on the right lane
  (in the direction: Antwerp, Einhoven, Heerlen, Aachen)
• exit no. 2: leave the motorway Aachen Laurensberg
• turn right in the direction Aachen (further see above ...)

From the Netherlands:

(e.g. from Maastricht-Aachen-Airport / Airport Brussels)

A4 drive in the direction Cologne

• first exit in Germany after crossing the border (exit no. 2) leave the motorway
• turn right in the direction of Aachen (further see above ...)

From Belgium:

(e.g. in the direction Liége/Lüttich)

A44 drive in the direction of Düsseldorf / Cologne

• to the motorway intersection Aachen
• there get into the right lane and cross the A4
• on the A4 change in the direction of: Antwerp, Einhoven, Heerlen, Aachen
  (right lane)
• exit no. 2: leave the motorway Aachen Laurensberg
• turn right in the direction of Aachen (further see above ...)