Car rental agencies rent automobiles for short periods of time (generally ranging from a few hours to a few weeks) for a fee. 

Some offers for Car rental in Dresden are listed below:
http://www.billiger-mietwagen.de/Mietwagen-Dresden.html  (Price comparison between several providers)
http://www.europcar.com/car-rental-GERMANY-DRESDEN.html  
http://www.enterprise.de/car_rental/deeplinkmap.do?cnty=DE&gpbr=G618&bid=004  
http://www.hertz.de/rentacar/mietwagen/dresden  
http://www.sixt.de/mietwagen/deutschland/dresden  
http://www.lexautovermietung.de/  

Carsharing is a model of car rental where people rent cars for short periods of time, often by the hour. They are attractive to customers who make only occasional use of a vehicle, as well as others who would like occasional access to a vehicle of a different type than they use day-to-day. Carsharing offers a good solution to be mobile without having an own car. For this purpose you purchase a claim for a vehicle, only when you need it. You can decide on the period of use.  You can choose your city between various starting-points in the city, the vehicle type as well as the period you need the car. 

Some offers for Carsharing in Dresden are listed below:
http://www.flinkster.de/   (Service provided by Deutsche Bahn)
http://www.teilauto.net/carsharing.php?f=1   (Service co-operating with Dresdner Verkehrsbetriebe AG)
https://www.greenwheels.com/de/Home/Privatkunden/Home.html (Service co-operating with Dresdner Verkehrsbetriebe AG)