If you're planning to use the local busses in Karlstad, or perhaps travelling outside Karlstad with bus you cannot pay by cash. You can pay by getting a bus card or by text message (SMS).
There is no underground or anything like it in Karlstad as the city is too small to have any such. Nor are here any trams. The public transportation system mainly consists of buses and the system of lines is well built.
The local buses that cover Karlstad and it's different local urban areas (such as Kronoparken with the University, Norrstrand and Våxnäs which are all part of the main Karlstad) but not outer urban areas like Ulvsby or Molkom some 10-20 km away all start at the main square and goes circlewise. All buses heading to the eastern parts of the city start at the NORTH side of the square facing east and all those heading to the western parts of the city starts on the SOUTH side heading west.
The are large digital boards telling you when your bus will be arriving. There are far more buses during mon-fri from about 6 AM to abput 7 PM than the rest of the time.
The regional buses all start at the main bus terminal in Karlstad, which can be found at the west end of Drottninggatan. There is a stop for some of the local buses there too. It would take about 10-15 minutes to walk in a normal pace between the two starting points.
All the timetables for these buses, as well as for the local buses in nearby cities such as Kristinehamn can be reach through the web site provided.
From late spring to early automn (about mid may to late august or early september) you can borrow a bike for FREE at the tourist booth beside the city Square, in front of the "Ticket" travel agency.
They only ask some kind of proof of identity (not sure what goes and what doesn't but your Passport number and name would probably do) and then you can use it for as long as you like during that day.
Karlstad is situated on the Stockholm-Oslo railway line, just about in the middle of it. Unfortunately there are far fewer trains than before but you can still go between the two capitals.
Tickets can be purchased from the national railway line, SJ.
The train station is situated right in the city centre, a short walk from hotels like Plaza, Comfort Inn, Stadshotellet and many others. With a minutes walk you are right on teh shopping street in Karlstad and with even a shorter walk you'll reach the first pub, The Woolpack Inn. (See a nightlife tip for that).
You should also take a minute or two to admire the architecture of the station itself, which is one of the prettier buildings in the city.
We took a train from Oslo to Karlstad then from Karlstad to Stockholm.
The trip from Oslo took about 3 hours. And the trip from Stockholm took about 3 hours too.
The trains were very clean and there was amazing scenery the whole trip...
Near the city hall there are a place to rent bicycles to travel around Karlstad, as it is flat you can enjoy the city using it.