Leipzig is easy to reach by rail, road and plane.
Airport Leipzig-Halle (LEJ):
You can fly directly to Leipzig from several cities in Germany or from Zurich, Vienna, and Istanbul. There are also flights from London Stansted (Ryanair) and Moscow Vnukovo (Pobeda).
To get to the city center from the airport, take the municipal railway (S-Bahn) https://www.bahn.com/en/view/index.shtml line S5 or S5X (southbound in the direction of Zwickau), which leaves Leipzig-Halle Airport every 30 minutes. There are three central stops: Leipzig Hbf (Hauptbahnhof/main station), Markt (market place), and Wilhelm-Leuschner-Platz.
A taxi ride from the airport to the city center costs about €40.
You may also consider the two airports in Berlin (especially Schönefeld, which has many cheap flights):
Berlin Tegel: http://www.berlin-airport.de/en/travellers-txl/to-and-from/buses-and-trains/index.php
Berlin Schönefeld: http://www.berlin-airport.de/en/travellers-sxf/to-and-from/buses-and-trains/index.php
The regular return ticket by train from Berlin to Leipzig is €100 (but if you book early, you may get a cheaper price).
By train or bus
Leipzig is conveniently located on the Munich-Berlin train line and on the Frankfurt-Dresden line. ICE trains from Berlin take 70 mins, from Frankfurt 3 hours, from Munich 3.5 hours. Some further travel times by train: Paris 7.5 hours, Warsaw 9 hours, Amsterdam 7.5 hours, Prague 4 hours, Copenhagen 8.5, Brussels 7 hours, Basle 6 hours.
If your train trip within Germany is longer than Berlin-Leipzig, you can book a special "Event Ticket" with Deutsche Bahn (DB):
One-way trip for a specific train (subject to availability):
Second Class 54,90 €
First Class 89,90 €
One-way trip fully flexible (always available):
Second Class 74,90 €
First Class 109,90 €
You can get more information here.
Besides this offer, DB has other special offers (saver fares "Sparpreis/Super-Sparpreis") which may be even cheaper than the Event Ticket.
For bus connections, see especially flixbus.com.
Approaching Leipzig from the north, via national route (Autobahn) A9, change to A14 at Schkeuditzer Kreuz in the direction of Dresden. Follow A14, then take exit Leipzig-Mitte, and follow road B2. Approaching Leipzig from the south or east, change from A9 or A14 to A38 and take the exit "Leipzig-Süd", then follow the B2.
Transport in Leipzig
Leipzig has a compact city centre, which is easy to maneuver on foot. There is also a very good tram and bus system.
All conference participants will have free access to the public transport system from August 20 (Tuesday, 12:00h) through August 25 (Sunday, 12:00h) (including travel from and to Leipzig-Halle airport).
Taking taxis is not advisable because they are quite expensive in Germany (about €25 for ten minutes). The main railway station (Leipzig Hbf) is just about north of the city centre and 5-10 minutes walk from the venue.