Public transport in Berlin is very reliable and there are numerous train stations in the vicinity of Spreespeicher.
The closest S-Bahn is Warschauer Straße. It is a 25-30 minute journey from Hauptbahnhof, the main train station in the city centre, on the S3, S5, S7 or S9 lines.
The (free) Citymapper app is available in Berlin and is helpful if you have an internet connection. There are also many reputable taxi companies well as numerous ride-hailing apps (including Uber and MyTaxi) with a presence in the city.