From Essen central station it takes 15 minutes to get to the hostel by foot. Otherwise, you can use the trams 107 and 108 to the stop "Viehofer Platz" or the trams 101, 105 and 106 to the stop "Rheinischer Platz". Both stops are 2 minutes by foot.
There are some parking spots on the roadside of the hostels that require you to pay a fee as well as underground parking opposite of the hostel that also requires a fee. At the end of Kastanienallee is an affordable parking facility (Parkhaus am Weberplatz - Wolf).
The next airports are in Düsseldorf (DUS) and in Dortmund (DTM). From both airports it is quite easy to get to Essen central station by train.
You can reach the Messe Essen within 15 minutes using the metro.