To create this support, use a spun poly-fiber product. This is marketed by several manufacturers, including Woodland Scenics which is available at most hobby shops. You can also find this in other craft stores.
Since the forest seen here is part of a night scene, the green Woodland Scenics fiber was painted flat black with spray paint first. You may be able to find darker fiber from other brands, or you can paint this any shade you wish. For daylight scenes, the green color is not objectionable.
Stretch the fiber into a fine and fluffy net and spread it across the tops of the trunks. Work the fibers a little further down the trunks on the foreground trees to create more detail and places for foliage later.
The web will probably entwine with the twigs enough that no additional adhesive is necessary.