By plane:
You can get to Leipzig via the Leipzig-Halle International Airport. Numerous European connections offer direct flight to and from Leipzig; more than 40 airline operators fly from Leipzig/Halle International Airport to close on 100 destinations. Please keep in mind that these are mostly European destinations. 
However, there are direct connections to the international hubs at Frankfurt, Munich, Vienna and Paris CDG, which allow numerous destinations worldwide. 

From the airport you can take the intercity train (ICE) to Dresden, which will stop at Leipzig Central Station. The cheaper and faster option would be to take S-bahn 5(x) in the direction of Zwickau (Sachs) Hbf. The S-bahn runs more often than the train, and costs only € 4,90. On the way to the city center, the S-bahn will also stop at Leipzig Messe, where the conference center is located. The journey to the Congress Center Leipzig takes about 8 minutes, and from there another 8 minutes to the city center.  
The taxi journey from the airport to the conference center also takes about 10 minutes. 

By train:
Leipzig's Central Station is one of Europe's largest railway terminal stations. Besides being an impressive architectural highlight, the station is located in the middle of the city, with hotels and restaurants within walking distance. 

The ICE trains provide good direct connections to all major cities in Germany. For example:

Berlin:  hourly service - ride of 1 hour
Frankfurt: hourly service - ride of 3 hours
Hamburg: hourly service - ride of 3 hours
Munich: hourly service - ride of 4,5 hours
Dusseldorf: hourly service - ride of 5,5 hours

Instead of flying into Leipzig/Halle International Airport, you can consider flying into one of these German hubs, and then taking the train to Leipzig from there.  

Getting around in Leipzig

The Congress Center Leipzig is located right in the middle between the airport and the city center.
From the city center, it takes about 20 minutes to go to the conference center, by taking tram 16.  
Regular timetable of tram 16 towards the CCL
Regular timetable of tram 16 from the CCL to the city

Extra trams will be available during the start and at the end of a conference day to ensure you will get to and from the CCL in time. Timetables will be available shortly. 

With your badge, you can get around in the city of Leipzig. Upon showing your badge, which has the logo of the MDV and the Leipzig Transport Bureau included on it, you will have free usage of public transportation (tram, bus, S-bahn) within zone 110 of the city of Leipzig. This is only valid for the period 12 - 17 August. There will be transport maps available in your conference bag. The Airport is not included in zone 110.
Online map of Zone 110.