Most foreign flights arrive at the Arlanda airport. To go from the airport to the Central station you can either choose the rapid train (faster and more expensive) or the airport coaches (slower and cheaper). There are also Bromma Airport and Skavsta Airport. These are mostly used by low-fare airlines. Skavsta is used by Ryan Air and is situated rather far from Stockholm although there are buses taking you from the airport to the central station. Bromma is close to the city and you take the bus from here as well.
Of course you can also take a taxi from the airport to the hotel, but since it is a rather long distance, you should make sure to get a fixed price and not use the taxameter. As an indication, the fare to go from Arlanda to the hotel with the TRANSFER taxi company is 773 SEK.
From the Central station you take the commuter train to the station Handen, a trip which (normally) takes less than 25 min. Information about the commuter trains can be found at http://sl.se. There is no English version, but you will find a Google translate function included in the page. As expected, this function works fairly well, but creates some amusing effects. At the Handen train station you take the exit near the rear end of the train, cross the tracks on an indoor bridge, then turn right when you get outdoors and continue along the row of houses. The hotel, Quality Hotel Winn Haninge, is situated a few hundred meters ahead. See this aerial photo for further information: