Though it’s a very "walkable" city, Gothenburg has an impressive and modern public transport system comprising largely of an enormous tramway, but also buses and commuter trains. It’s inexpensive and easy to use, so on the days where you don’t fancy a walk or cycle, it will get you where you need to be nice and quickly.
With the two major airports within 20 minutes of the city - Landvetter Airport (GOT) and Gothenburg City Airport (GSE) - being fed by most big European airlines, it’s very easy to get here. There is a city bus for each airport which takes around 20 minutes to get to the centre and costs €8 for a single.
If you’d rather get straight to your door, you can grab a taxi from outside Arrivals for €35-40. It’s a lot more expensive, but if it relieves the stress of travelling on your first day, it might be worthwhile.
Other major Scandinavian cities like Oslo, Stockholm and Copenhagen are all connected by train to Gothenburg. If you find a cheap deal to fly to one of these neighboring cities and then take the train into the Gothenburg city centre, go for it! You can easily get the tram from the central train station and travel close to your accommodation, no matter where in the city that might be.
Though usually less common than arriving by plane, the Stena Line has a fleet of over 35 ships that sail between Scandinavia, the UK, Ireland and Latvia - if it’s a convenient option for you, then just sail straight on up into the city.
The infrastructure for trams in Gothenburg is second-to-none, and the buses do pretty well too. There are over 200 trams and 12 different routes spanning the entirety of the city. There are so many that you shouldn’t ever be waiting more than 10-15 minutes during the day, though fewer services run overnight.
The main job of the buses is to reach those areas which the trams do not. They also penetrate further into the city’s suburban surroundings, so are a good option if you’re going quite a long distance.
There are a few options. You can purchase a City Card, use a prepaid card, buy day travel cards or simply use cash/card on the tram. City Cards are more for tourists, as they’re quite expensive and offer discounts to local attractions. Day travel cards offer unlimited use of all public transport for one or three days - again, more for tourists than day-to-day locals.
The most common method is to use your card on a per-journey basis. However, this is not an option (yet) on buses, so you might want to carry a pre-paid card for any unexpected bus journeys which crop up.
Gothenburg has loads of dedicated cycle paths and flat roads, so it’s a cyclist’s dream. Don’t worry about taking your bike out with you either, as the City Bike scheme - called Styr & Ställ - is quite cheap and easy to use. You need to pay around €25 to sign up for a "seasonal" pass (i.e. annual pass), Once you’ve received your card, the first 30 minutes of any journey are totally free. As long as you return your bike within 30 minutes (even if you remove it immediately after again) you’ll get free cycling all year round.
Though it’s in Swedish, you should consider downloading the Cykelstaden app on android (or Apple, if that’s your thing ;)), which shows you where all the station are, as well as maps of the city and its cycle paths to help keep you right.