The Imperial Palace East Gardens are accessed through the Otemon Gate of the Imperial Palace. From Otemachi Station, take exit C10. From here, walk straight until you reach an intersection; you will see a sign for Otemon on the road, and directly in front of you, you can see the foliage of the Imperial Palace. Cross the road and you will see the Otemon Gate.
From Tokyo Station to Otemachi Station:
Take the Marunouchi Line direct to Otemachi Station (2 minutes, ¥170)
From Shinjuku Station to Otemachi Station:
Take the Marunouchi Line direct to Otemachi Station (20 minutes, ¥200)