Hi camy,
1) Decide on a budget - i.e. how much you want to spend on a property; in doing that, allow for approx. 10-13% in acquisition costs (acquisition tax, commissions etc).
2) Think about a location where you would like to invest. You seem to have done this already. Why do you want to invest in Düsseldorf? Would you also be interested in other areas?
3) Decide in what type of property you would like to invest - residential, commercial, mixed etc.
4) Obtain information on properties in the desired location and price range.
5) Travel to Germany and view the properties.
6) Depending on property type, price etc. you may then want to carry out checks on the properties (lease agreements, structural surveys etc).
7) Negotiate price.
8) Once a price has been agreed, a notary is commissioned to draft the contracts.
9) Once the contracts are drafted, they are typically signed by both parties in the presence of the notary (the notary is normally paid by the purchaser, the costs are included in the 10-13% acquisition costs mentioned above).
10) The contracts conclude, i.e. the property changes ownershipd and the purchase price becomes due for payment, a few weeks after the signing.
Obviously, this is only a rough overview of the various steps. What exactly happens depends very much on the individual transaction. Please feel free to ask specific questions! ;-)