Best way to get from Berlin to Leipzig (and back)

The answer to "best way", almost anywhere in Germany, is always, "By train". There are ICEs running between Berlin and Leipzig in just over an hour. If you can commit to a specific train (date and time) its €19/p each way. If you don't want to commit, you can do the trip by regional trains in 2½ hrs for €42, RT, with a Quer-durchs-Land-Ticket (all day pass for a single person), or, on a weekend day, for €40 with a Schönes-Wochenende-Ticket.

Actually nothing should be added to Lee's great advice. But just for the record BerlinLinienBus.de operate a bus line between Berlin's Central Omnibus Station across from the fair grounds to Leipzig airport (which is about 30 minutes outside town). Journey time is 1:45 hrs one-way and fare is €30 one-way... again, just for the record. By the way: As you've probably heard already Leipzig's Central Train Station already is your first major sight in town...

Yes you could take an ICE from Berlin to Leipzig. And they go quite frequently every hour. However, there is also the Interconnex, a private train company that runs twice a day on this line and takes the same time as the ICE. But it costs less then the Bahn tickets. Special saving tickets start at 14 Euro (online booking ahead of time) up to 23 Euro when bought sitting already in the train. www.interconnex.com