So if you want to pick up lots of beverages for your birthday party next weekend and don't feel like hauling them back in public transport or with your bike, you can just rent a car for x minutes, go shopping, drive home, park it in a reserved place in you neighborhood.
The price model of most providers is however not the best for the visit grandma in the countryside problem, but most of those carsharing companies have special tarifs with rental providers, so you can get a relatively cheap car for the weekend.
The way it technically works is almost always the same: You sign up and you get an RFID Key Card. You go on the internet or use an App to see if a car is available in your area and book it. You go to the car, open it with you keycard and find the keys in the glovebox. Sometimes you have to put in a PIN first. Some providers have a monthly fee, some just charge the usage.
Some Websites for those interested:
www.car2go.com - Backed by Daimler - Smart Cars even in some NA cities
www.greenwheels.com - indipendent, has been around for ages
www.flinkster.de - Backed by Deutsche Bahn (german railways), they also have bikes for rent
www.stadtmobil.de
www.drive-now.com - Sixt (biggest german rental firm) and BMW - nice 1-series and Minis
www.web.quicar.de - Volkswagen got into the business,too
+ multiple regional projects