So how did someone from West Berlin travel to, say, Frankfurt by car?
There were few approved transit routes from West Berlin to West Germany. So you could get a transit visa (which you had to pay for in west german currency) upon getting on one of those routes and present it to exit the GDR again (you weren't allowed to leave the transit route midway, and if you took to long to pass through, you'd be questioned). Note that transit between West Berlin and West Germany is different from simply crossing between the two Germanies[0], which was relatively easy for est german citizens, but particularly difficult to do for east german citizens.
What was to stop someone from East Germany doing the same thing? The wall only went through the city, right?
The wall may have only gone through the city, but there still were border checkpoints[1] outside of Berlin.
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There were few approved transit routes from West Berlin to West Germany. So you could get a transit visa (which you had to pay for in west german currency) upon getting on one of those routes and present it to exit the GDR again (you weren't allowed to leave the transit route midway, and if you took to long to pass through, you'd be questioned). Note that transit between West Berlin and West Germany is different from simply crossing between the two Germanies[0], which was relatively easy for est german citizens, but particularly difficult to do for east german citizens.
The wall may have only gone through the city, but there still were border checkpoints[1] outside of Berlin.
[0] http://en.wikipedia.org/wiki/Crossing_the_inner_German_borde... [1] http://en.wikipedia.org/wiki/Inner_German_border