There are many ways how to get around in Gothenburg, but in my opinion, cycling is the best one!
It´s practically free, you´re doing something for your health, no traffic jams, so you are never late, in many times you´re faster than tram and you get to know the city from totally new perspective. A bicycle was one of the first things I bought, when I came to Gothenburg. For a price of 1000 SEK I got single-speed in very good shape, which I am using ever since on daily basis. 1000 SEK is a standard price for a second-hand bicycle, but you can get one much cheaper or even for free (which I didn´t know back then)!
On Blocket, an online second-hand shop, the price starts somewhere between 400 and 600 SEK. Those bikes are usually in worse condition or they´re children size (it´s not so obvious from a picture sometimes), but if you´re staying only for one semester, it can do the job. You can find really decent bike for 800-1000 SEK, which will run forever with proper maintenance. There is of course “a free” option and no, I am not talking about stealing. I am talking about Cykelköket Göteborg aka “bicycle kitchen”. Cykelköket is an open workshop where you can learn how to fix bikes and for small membership fee you´ll get a bicycle for free. They usually have a bunch of broken bicycles in the workshop, which they collect in Göteborg. The condition really differs, some are good just for parts, others need only to pump a tire. The workshop is well equipped and there is always helping hand around. Cykelköket is located in Vegagatan 1 and open every Tuesday, Thursday and Saturday. Check it out!
Another option is to rent a bike, which I never tried, but it seems like a good option if you need a bike only occasionally. It´s call Styr&Stall and here you can find more information.
I am living near Frölunda Torg and I´m cycling to HDK (Valand tram stop) every day. It takes me about 25 minutes, even though Frölunda is a bit far from city center. For a while I was cycling from Frölunda to Hisigen and it wasn´t bad at all! So if you´re worrying about distances, don´t be:)
Gothenburg is criss-crossed with bicycle paths and you´re free from traffic jams. There is a nice little cycling map in every Service Center, I would recommend to get. Great if you need directions, while you´re cruising streets of Göteborg or going for a ride along the coast!
All the best,
PS: Don´t mind the weather and go cycling today!;)