I don't recall any peculiar rule. You are supposed to walk on the sidewalk and to cross streets only when the pedestrian sign is green (unlike the UK, if that's where you come from). You can receive a small fine for failing to do so. It's not as bad as Amsterdam but do beware of bike lanes and treat them like streets (look right and left before crossing, don't walk or stop on a bicycle lane if you don't have to).
One thing that might be of particular interest to you are the 20 “green walks“ through the city. It's a project to identify and mark major ways across Berlin for bikes and pedestrians using parks, canals and quiet streets to minimise interactions with motorised traffic. Some of them can be used to link key parts of the centre, others provide picturesque walks in outskirts.
The website provides a lot of info in English, coordinates to download and an overview of each walk with Open Street Map. On the ground, these “green walks” are marked with white and blue signs with a number.
The public transit network in Berlin is also quite good and the city is larger, greener and less dense than many European capitals. So even if you are used to walk in cities, the distances might surprise you. Don't hesitate to use public transport as well. Bus line number 100 is notorious as a cheap way to check the main sights for the price of a regular ticket, without paying for a tourist bus/guided tour.