In order to drive a car in Germany it's necessary to have a licence which must be with you at all times while driving.

Short-time stay in Germany

If you have a valid national or international driving licence, you may drive those vehicles in Germany which your licence permits. This is true even if you have not reached the legal age for driving in Germany.

It's not necessary to get a translation of an international licence. This is not the case with national licences. National licences must normally be translated if issued

    in a country which is not a member of the EU or EEA
    in a language other than German
    in a country that does not comply with the agreement on road traffic

Exceptions are Andorra, Hong Kong, Monaco, New Zealand, San Marino, Switzerland and Senegal. The translation must always be with you when driving.

Long-time stay in Germany

If you have a licence from a member state of the EU or EEA, it is also valid in Germany until it expires. If your licence is no longer valid after your transfer of residence to Germany because of the above-mentioned limitations, you can still drive for six more months in Germany. You must file for an extension of your licence in this time period.

If your licence was not issued by an EU or EEA country, it is still valid in Germany for six months after your move. After this time your driving permit is no longer recognised and a licence issued in Germany is required. The requirements to obtain a German driving licence depend on the country where your licence was issued. Please contact the driving licence office in good time to obtain a driving licence.

Ordnungsamt
Fahrerlaubnisbehörde
Hauboldstraße 7
01239 Dresden

Opening hours: Monday and Friday: 09:00 am -12:00 noon, Tuesday and Thursday: 09:00 am -1:00 pm and 3 pm - 6 pm, Wednesday: closed.

Driving a vehicle with a foreign licence not recognised in Germany is considered the same as driving without a licence and is punished accordingly.

Source: http://welcome.dresden.de/en/life/transport.php