This stitch is just an extension of the radiating stitch. You can say it is like mirror images of the radiating stitches, made to look like a lantern. The Lantern stitch can be used to make simple motifs or base for extended variations. It can be used nicely over even weaved fabric as well.

You need to know the radiating stitch to be able to continue with this tutorial. 

 lantern_stitch_1    lantern_stitch_2
Fig 1: Start by making radiating stitch   Fig 2: Then, make a mirror image of the radiating stitch, as shown. 
lantern_stitch_3    lanter_stitch_4
Fig 3: Now, bring the needle out through B, in through A, and out through C. This process will start connecting both the radiating stitches, giving it a lantern look. Connect the remaining points.    Fig 4: A finished lantern stitch looks like this.