To separate stems from leaves, grab the stem in one hand close to where the leaf starts. With the other hand, fold the leaf in half on itself and pinch the two halves together while pulling away from the stem.
The tearing method should work very well for kale, but other leaves may need a knife. If tearing isn't working well, lay the leaf on a cutting board, fold it in half with the stem on one side and make one cut along the stem to cut the leaf away. Discard kale stems. Chop all other stems into bite-sized chunks.