The Germans were pretty effective and methodical at dealing with partisan and local resistance, though they never were able to completely defeat it. The most partisan activity took place in Yugoslavia, France and the Soviet Union, where the Gestapo, the SS and the German Wehrmacht used trial and error combined with brutality to attempt to deal with them.
Reprisals were the most common method, where 50 civilians would be killed in the nearest village for every German shot by the partisans. This of course put a gigantic disincentive in place and created some localized resistance to the partisans, or sometimes led to civilians giving the Germans information about the resistance. This was fairly rare, however.
In Czechoslovakia, following the assassination of SS Reichsprotektor Reinhard Heydrich in 1942, the nearby village of Lidice was razed, the males in the town were executed, and the women and children deported to concentration camps. This was more extreme than most German reactions, but also seemed to be more common on the Eastern Front, including in the Soviet Union.
The Germans were also very effective at gathering intelligence, in part because their police organizations and SS had absolute authority over local populations and could use any method of intelligence gathering or torture that they wished to.