The best way to get to Üsküdar is by using the ferry or Marmaray subway line.
If you’d like to cross over to Üsküdar on the Asian side, go to the “Karaköy” or “Eminönü” station of the tram line T1, and go to the ferry pier that crosses over to Üsküdar. It takes 20 mins by ferry to get to Üsküdar from Karaköy or Eminönü.
If you are going from Taksim square area, take F1 funicular line from Taksim square down to Kabataş, and take a ferry from Kabataş pier to Üsküdar, which also takes about 20 mins.
If you are going from the Galata area, walk down to Karaköy or take F2 funicular line down to Karaköy, and take a ferry from the Karaköy-Üsküdar pier.
If you would like to cross over by subway, or if the ferries are not working due to weather conditions, you can also take the subway. Take the tram line T1 and go to “Sirkeci”. In “Sirkeci” transfer to the Marmaray line and go to Üsküdar. It is only one stop from Sirkeci station with the Marmaray metro line, so you can switch continents in about 5 mins via Marmaray.
If you are coming from Beşiktaş, simply take a ferry from the ferry pier of Beşiktaş, and you will be in Üsküdar in 5-6 minutes since these two districts are geographically facing each other on the Bosphorus.