The Studierendenwerk Berlin does not always offer internet access in the accommodations because it does not belong to the standard housing facilities in Germany. There is currently internet access in dormitory Halbauer Weg, but not in dormitory Goerzallee. An internet connection is supposed to be implemented during the year 2019.
In addition to that, all students will have access to the computer labs and the Wi-Fi network available on campus. Furthermore, there are many affordable internet cafés in Berlin, as well as cafés that offer free wireless for their customers. You can arrange an individual contract with a telecommunication company to get access to the internet. There are different telephone companies in Germany and quite a wide range of different offers, but most contracts run for several months (usually 24 months). Therefore, please pay close attention to the details of the contract so that you are not bound for too long, as it might be difficult to terminate the contract prematurely.
Another solution is to purchase a “surfstick” - a USB-stick-like modem that allows you to connect to the internet via cell phone networks. Many cell phone providers have surfstick options, but only some have prepaid options without a minimum contract duration. Also, there are data volume restrictions and the sticks themselves can be quite expensive (50-70€), so make sure to go over terms and conditions carefully.