Owing to its central location, transportation to the Galatasaray High School is fairly easy.
Tunnel: The Tunnel, which is the oldest surviving underground urban rail line, connects Karaköy and Beyoğlu. For those coming from the Anatolian side via the Kadıköy-Karaköy or the Üsküdar-Karaköy ferries, taking the funicular is the fastest way to get to the İstiklal Avenue. After you get off the tunnel, turn right towards the İstiklal Avenue (You should be able to see Shake Shack and the Şişhane subway station on the right) and walk ca. 600 meters until you get to the Galatasaray Square.
Subway: The Galatasaray High School is placed in-between two subway stations: Şişhane and Taksim. While you can get off at either of the stations and walk along the İstiklal Avenue, it is advised that you use the Şişhane stop instead of Taksim instead as it is about 30% closer to the school (Please note that it’s downhill from Taksim and uphill from Şişhane, although it’s a relatively slight slope.). You should be able to spot the school once you get to the Galatasaray Square.
If all else fails: Just find a way to get to the İstiklal Avenue and walk along the street. Galatasaray Square is in the midst of the Avenue and the school is very noticeable with its colossal embellished doors. (Whomever you ask, they’ll show you anyways.)