If you are coming from outside of Europe it is likely that you will be landing in Frankfurt (there is a train that takes you from the airport to the central station (Hauptbahnhof)). If you come from within Europe there is a low cost Airport in Baden Baden (that has ryanair: [http://www.ryanair.com/]). AVOID at all costs the trains in Germany, they are very expensive, instead try this bus company that goes between the main cities (usually stops at the main station, in Frankfurt it does): [http://meinfernbus.de/]. (you can buy the ticket online). To go from Baden Baden airport to Stuttgart, you need to pass through Karlsruhe, Meinfernbus will take you from Karlsruhe to Stuttgart, but to get to Karlsruhe you are advised to check [http://en.kvv.de/] (here you will find the prices, hours, and all the information to make the cheapest trip from the airport to Karlsruhe). If you are dum and decided to catch the train with Deutsche Bahn, follow at least this advice and buy the ticket in advance since it is quite cheaper [http://www.bahn.com/i/view/GBR/en/]. There is also the hypothesis that you are rich and you had the money to go directly to Stuttgart Airport, if that's the case, great for you, you rich asshole.  

If you are coming from outside of Europe it is likely that you will be landing in Frankfurt (there is a train that takes you from the airport to the central station (Hauptbahnhof)). If you come from within Europe there is a low cost Airport in Baden Baden (that has ryanair: [http://www.ryanair.com/]). AVOID at all costs the trains in Germany, they are very expensive, instead try this bus company that goes between the main cities (usually stops at the main station, in Frankfurt it does): [http://meinfernbus.de/]. (you can buy the ticket online). To go from Baden Baden airport to Stuttgart, you need to pass through Karlsruhe, Meinfernbus will take you from Karlsruhe to Stuttgart, but to get to Karlsruhe you are advised to check [http://en.kvv.de/] (here you will find the prices, hours, and all the information to make the cheapest trip from the airport to Karlsruhe). If you are dum and decided to catch the train with Deutsche Bahn, follow at least this advice and buy the ticket in advance since it is quite cheaper [http://www.bahn.com/i/view/GBR/en/]. There is also the hypothesis that you are rich and you had the money to go directly to Stuttgart Airport, if that's the case, great for you, you rich asshole.  

Ok, let's imagine now, that you have safely arrived in Stuttgart. There are 4 possible points you may be: Stuttgart Airport (if you are rich, or if you came by one of the lines of meinfernbus), Stuttgart Main Station (if you came by train), Stuttgart Zuffenhausen (if you come by meinfernbus that is the most likely stop), or Stuttgart Obertürkheim (other meinfernbus stop). From here you must know that there are several kinds of urban transportation in Stuttgart, but for now you only need to care about one: the S-bahn (which is the urban train system, NOT trams: those are the U-bahn). From all these locations you have S-bahn, and so does your destination the S-bahn station: Universität. The S-bahn map is quite clear and all stations are equipped with machines that can be set into english, so I won't get into detail here.  

Ok, let's imagine now, that you have safely arrived in Stuttgart. There are 4 possible points you may be: Stuttgart Airport (if you are rich, or if you came by one of the lines of meinfernbus), Stuttgart Main Station (if you came by train), Stuttgart Zuffenhausen (if you come by meinfernbus that is the most likely stop), or Stuttgart Obertürkheim (other meinfernbus stop). From here you must know that there are several kinds of urban transportation in Stuttgart, but for now you only need to care about one: the S-bahn (which is the urban train system, NOT trams: those are the U-bahn). From all these locations you have S-bahn, and so does your destination the S-bahn station: Universität. The S-bahn map is quite clear and all stations are equipped with machines that can be set into english, so I won't get into detail here.