Hey Max .....
Here's what I do, though others may differ in their methods a bit. First A/B the cheesecloth in the desired colour. Lay it on the model in the approximate location that you wnat to locate it in. Using a brush to apply your mixture of white glue / water, liberally apply it to the cheese cloth until it is fairly good and wet locating it at the same time exactly where you want it. Allow it to dry, usually overnight. Dry brush the net for highlights. If you have a little "overflow" of the glue / water mixture, don't worry too much about it, it can be covered easily with normal weathering techniques. Complete the weathering with the rest of your kit.
As far as branches and stuff go, I've seen pics of them tied on with rope, stuck into nooks and crannies, crammed behind wire mesh, and in some cases even seen where the crew welded pieces (approx 6") of small guage pipe to hold the branches in place.
Happy Modelling and God Bless
Robert