To travel to Örebro, the best option is to fly to Stockholm (Arlanda Airport) and take the bus or the train from Arlanda to Örebro.
To take the bus, you have these two options:
You can also take the train from Arlanda to Örebro. This website can be used to check the timetable and book the ticket:
This page contains both bus connections and train connections to Örebro. The bus connections are those with 0 (zero) changes. The buses on this page are the same as those in number 1 above.
If you take the bus, the bus goes from Arlanda to Örebro. If you take the train, you have to take the train from Arlanda till Stockholm City and change trains there for Örebro.