Here is a common pattern of call and response which is found in many Blues songs. There are lots of variations, but memorising this pattern will enable you to play call and response very effectively with other musicians or vocalists. The first two responses are played over chord 1, while the third response is a turnaround. A good example of this format is the song "Sweet Home Chicago". Listen to Blues albums for other examples.
The most important thing to develop when working on call and response, is the ability to complement what the other musician is doing without getting in their way. A great way to practice this is to play rhythm while the other instrument is playing.
Here is another example. This time the response is played with chords, working in a similar way to a horn section.