Sorta depends on your gear... As mentioned above, some set-ups like Hennessy's aren't universal. For most gathered end hammocks with full bug nets you are correct: bug net encases the underquilt which cradles the hammock which has you and the topquilt inside. All of that is hung from the same suspension, while the tarp hangs from its own suspension (which will end up lower on the trees than the hammock's suspension).

Most every night, even no chance of rain, I pitch my tarp and smile when I can hear aerial debris ping off it.

Also, a pad is redundant (and less comfortable) if you have a warm enough UQ. The pad is a good low cost entry into colder hammock camping, but the beauty of the bigger buy (UQ) is that you are laying in just the hammock fabric- no pad wrestling or waking up cold cause you rolled off the pad. Preserves the comfort that converted me to hammocks in the first place.

Again, hammockforums is an invaluable resource. Lot of questions, experienced and varied answers, DIY plans and troubleshooting, trip reports, all that jazz. If you're more a visual learner, search around youtube for great instructional hammock videos by a character named Shug. They are informative and entertaining; I bet just typing "Shug underquilt" would dig up a good video or three.