Once you exit the airpot (TXL) you are at loading/unloading and drop off zone of TXL. That is also a massive bus stop with different bus lines to choose from.
Make sure to buy your bus card at one of the machines before you board your bus. The machines are located outside, at the bus terminal. You cant miss them, they’re big, boxy and yellow. Its 2.80 Euros one way plus transfer.
I took TXL 147 bus. If you see it on the Rail map, you see that it drops you off at the first available train station. From there you can work out where else to go. I kept going because I missed my stop. However, the train station shows your future stops. I sat on the train until I got to Hauptbahnhof station, which is one of the main stations with many lines to choose from and transfer.
From here I took the S5 orange line (direction Strausberg Nord) to the next stop and transferred to the U6 purple line (Alt-Mariendorf direction) and got off at Statemitte station. Here I resurfaced and looked for my hotel, which is the Hilton hotel.
Its easy once you get the hang of it.