The light looks like it might be resting on top. Depending on the screen, it could be strong enough to hold (you just have to make sure the screen does not get too hot under it). Either that or hanging it from the ceiling could work.
The branches I heard are possible to hold in place with thumb-tacks, on the outside of the vivarium piercing into the wood from the outside. This is assuming that the wood fits perfectly inside!
::EDIT::
Just noticed the plants... the bottom one looks like it's just resting there. The others COULD be attached to a back wall that is not screened, but I am not sure!