European licences work in Germany. Most others [sources needed] are only valid for half a year. Some of them can be transferred or converted. But as a rule of thumb for non-EU driving license holders: If you live in Germany permanently, you need to do a new licence in Germany.
how much it costs
There are several factors involved. You need to sign up with a driving school (Fahrschule), and you need to take a certain amount of minimum required lessons. These incur costs. Then there is the sign-up fee with the TÜV, who will provide the exam. There are fees for the theoretical and practical exams.
In 2017, you're looking at a minimum of between 1000 and 1500 Euros, depending on your location. In larger cities it might be a bit more expensive. If you need more lessons, or fail an exam, it will cost more.
how long it takes
Usually the process takes a couple of weeks at least. There are driving schools that offer crash courses. One required part is attending all 14 two-hour theory topic classes offered by your driving school. Driving schools are private businesses. Depending on the size of the town and the driving school company, they might run twice a week, with one topic every time, so 7 weeks at least, or they might have a rotation that allows you to do it in two weeks if you have enough time. There are places that do crash courses (hopefully not literally). You also need to then get an appointment for the practical exam. I'd plan a month in total minimum.
in what way driving knowledge/experience could simplify the process (reduce cost and time, see below)
If you are already comfortable driving, you can probably get by with the minimum required practical lessons. Those involve driving over land between towns, a couple of hours Autobahn and night drives. You cannot waive these. Sometimes a driving school will allow you to waive some or all of the theory classes if you have enough previous knowledge. But then again, the rules in Germany are very different from the US, so the theory part is actually relevant.
If you know someone with a car, you can practice at a Verkehrsübungsplatz for less money than the actual lessons. That does not replace the lessons though, but it can save some time. ADAC and various Verkehrswacht organizations offer those.
In any case never practice on an empty parking lot! Driving in public without a licence is a criminal offence.
