Duisburg is easily accessible by train. When I go there, I usually take the regional train from Cologne which takes about 45 minutes and also stops in Düsseldorf and Düsseldorf Airport. Apart from many regional trains to other cities, there are also ICE trains to Berlin, the Netherlands and other destinations.
The main station (Hauptbahnhof) is actually not among my favourites, I don't really like the atmosphere and there are usually a few shady characters hanging around there, but apart from being asked for a Euro, I never had any problems. I wouldn't like to be there at night, though.
There are several shops, eateries and cafés in the station, as well as toilets which need to be paid for.
The train station is only a few minutes walk from the city centre, but in case you need to go further away, there are always plenty of taxis waiting.
Duisburg has an excellent tram based public transport system once you figure out the complex ticketing system (see "warnings") and the way to change platforms as well as where trains actually stop in the city centre stations! The central station is the hub for most lines and the major (underground) stations are the ones with best map services of the greater Duisburg region if you need to plan your day. Bear in mind that one track used by several lines can mean that one line uses the front of the platform whilst another uses the back so do check where you need to wait. It is painted on the walls along the track and the screens indicating destinations will also give you a clue although sometimes those might confusingly give you all destinations on that track. There are several types of tickets, including for groups.
Duisburg could not be easier to reach, even those of us coming from Copenhagen can get there by direct night train :))) Smack bang in the Ruhrpot, Duisburg is on the main Hamburg to Heidelberg/Stuttgart line which also includes direct Dortmund, Essen and Cologne connections and distances are short between the latter bunch so a daytrip from there is also possible.
Public transport by trains, trams, buses and underground is very reliable. There are a variety of different options around, but as a rule of thumb it is always cheaper to buy a ticket valid for four journeys than just for one.
Most important thing to remember, however, is that you will need to stamp your tickets PRIOR to going on the transport. There aren’t a hell of a lot of check ups and you may even spend your whole stay in Duisburg without once meeting a conductor, but if you do meet them they will fine you big time if your ticket isn’t stamped. Not knowing this rule will not make them change their mind about the fine!