Information on visa regulations and on Germany in general can be found at the Federal Foreign Office. The regulations can also be seen here. Or you may want to take a look at "Make it in Germany".
As different types of visa exist (student, work, researcher, Blue Card, ...), we recommend that you check with your AWI staff officer which type would match the contract planned for you. They may then provide you with certain documents that you need for the visa application.
With your supervisor in AWI you should clarify if you will (also) need to enrol with a German university.
Make an appointment with the German mission in your country of residence as soon as you know that you will come to Germany. In some cases the visa application may be processed relatively fast, but in other cases the earliest possible appointment is several weeks ahead, and then the process itself may take several weeks, too, depending on the circumstances.
As soon as you obtain your visa, make sure to send a copy to your contact person in AWI's personnel department. They cannot issue the contract without a corresponding visa.