With the CAGED system for minor seventh chords you can play any minor seventh chord in five different positions on the guitar fretboard. If you haven't already, please have a look at the introduction of the CAGED system.
The CAGED system for minor seventh chords uses the open minor seventh chord shapes Cm7, Am7, Gm7, Em7 and Dm7, which haven't been introduced yet.
Minor seventh chords contain a minor chord plus the minor seventh. They have much less tension than the (dominant) seventh chords and sound similar to the major seventh chords, only a bit more melancholic.
Here are the five minor seventh chord shapes combined on the fretboard:
The numbers in the circles are the intervals / scale degrees. Please have a look at the introduction to intervals and chords if you haven't done so already.
Playing all the notes of a given chord shape is often impractical or inappropriate. Below are commonly used versions of the minor seventh chord shapes.
When in doubt: Here is an explanation of how to use movable chord shapes and here is help on how to read chord diagrams.