I started my hanging career with much the same set-up, although I had the 4,5x3m tarp!
With its original suspension, the hammock ties off to the tree thus (or at least that's how I did it): wrap the webbing straps around the tree - one going on each side. on the "front" side of the tree, secure them around the tree with a reef knot with hitches - same as for your shoelaces really. I remember reading that DD suggests, contrary to many other hammocks, that you should try to make it really taught. I changed the suspension rather quickly, because it's not that easy to gauge where it's centred between the trees.
I used a really long rope for the tarp - usually I ran it underneath to lift it as much as possible (because I'm a tall bugger). I usually just tied the rope around the tree wih a taught line hitch, then fixed the center tie-out of the tarp on the line with a klemheist knot using a loop of old guy line, which made it nicely adjustable.
The line running under the tarp gives you the opportunity to tie up the bugnet as well. You can, as suggested by DD, use a stick to separate the loops and create more room. Any stick will do, also one that you find in the bush. The hammock is originally supplied with shock cords for those loops, which is not bad to avoid tearing the bugnet as you get in the hammock.
From, IIRC, my first ever real camping trip in a hammock, in northern Ontario, Canada:
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