The closest international airport is Düsseldorf airport (DUS). From there, you can reach Essen conveniently by regional trains (in about 30 minutes, about 13 EUR per trip). There also are fast trains (IC/ICE) which are a little faster, and more expensive.
From Cologne/Bonn airport (CGN) you can reach Essen in a little more than one hour (with long-distance IC or ICE trains, about 28 EUR per trip) or one and a half hour (with regional trains, 20 to 25 EUR). Possibly you will have to change trains in Köln (Cologne).
Finally, you could consider flying in to Frankfurt airport (FRA), where many international flights arrive, but which is located quite a bit farther from Essen. From Frankfurt airport, you can reach Essen by train in about 2 hours by ICE trains, for about 95 EUR. There are some direct connections; otherwise you will have to change in Köln (Cologne).
Please note that tickets for regional trains are not valid in ICE, IC and EC trains. For the latter, you need special (and more expensive) tickets. The ticket vending machines show the available connections, and it's easiest if you buy a ticket for the exact connection you are going to use. See the local information page for more information on how to reach your hotel from Essen Main Station.
To check train schedules and fares, see German Rail.
There are some indications on the web site of the city of Essen.