While it isn't a problem around Konigstrasse, where pedestrians are so numerous they get right of way whether they are entitled to it or not, much of the rest of Stuttgart is as traffic friendly as a car city can be. Thankfully the excellent public transport system shields you from most of the traffic, but the rest of the time you will find yourself second best to the car. Just be aware that it is a little more difficult to walk from one part of the city to another than some other places, and take the subway or tram if the pace gets too slow.
When driving here you need to be very careful and concientious.
The yellow diamond shaped sign means that you are on a priotity road and you have the right of way. If you are not on the priority road you have to yield to the right. Even if is a smaller side road or alley you still yield to the right.
Do not cross over a solid white line.
If you see brake lights, brake right away as a caution to the people behind you. Sometimes you can go from 120km to 50 and it's very common. Rule: See brake lights: BRAKE.
Try to keep up with the flow of traffic. Going too slow can be just as harmful as going to fast.
There is major major traffic in Germany especially in the West and you may end up in a traffic jam for hours.
The fact that the autobahn is open for high speeds is true but you have to know what you are doing. Some cars go up to 180 miles per hour in the fast lane and if you in that far left passing lane you have to pay attention to cars coming up behind you.
ONLY use the left lane to pass in, it's a law.