The Germans knew of the British Radar (RDF) system before the start of the war, but failed to appreciate how sophisticated the integrated RAF command & control methods were - they had their own system too - Freya and Wurzburg, first used against the RAF raid on the naval yards at Wilhelmshaven in December 1939.

http://en.wikipedia.org/wiki/Battle_of_Britain

http://www.amazon.co.uk/The-Most-Dangerous-Enemy-History/dp/1845134818

Best book on the BoB - in my humble opinion.

http://www.amazon.com/Bomber-Command-Max-Hastings/dp/0330513613

Excellent overview of the (British/German) technical struggle in the skies of WWII.

The Germans both knew a lot about Allied radar tech and used radar extensively themselves. The use of radar by the RAF was know, in fact radar stations were regularly targeted.

Radar warning receivers ('Funkmessbeobachtungsgerät') where widely used as early as 1939/40, especially on Kriegsmarine units including submarines. Throughout the war it was basically a race between the radar engineers and the radar detector engineers on the other side. To be able to properly detect enemy radar the wavelength has to be know beforehand as until 1944/45 German detectors were not able to cover multiple wavelengths. A lot of information about allied radar tech came from bombers shot down over German controlled areas and the analysis of their on-board systems. One of the few examples covered by the english Wikipedia is the Naxos, used from 1943 onwards in night fighters and U-boats.

Radar itself ('Funkmessgerät') saw even more widespread usage, from the naval and stationary units at the beginning of the war to much smaller and sophisticated systems used in the night fighters of the late war. 1938 the a radar unit was installed on Admiral Graf Spee and by 1945 every Kriegsmarine units was equipped with radar, from U- and S-boats to the remaining capital ships. This gives a good overview of German naval radar throughout the war.