The big round plastic tube goes into the tank- that is the part actually used to clean the gravel. You need to have a bucket (or a handy sink or toilet) ready for the other end - the flexible plastic tubing - which is where the water and crud will drain out from.
To start it working, you can either suck on the end of the flexible tubing and then just take your mouth away quickly and point the tubing into the bucket as soon as the water starts coming through the pipe (which is what I do), or you can simply submerse the whole thing completely under water in the tank, then lift the flexible tubing part out with your thumb over the end, postion it over the bucket and let go. Either way works fine; the water will continue flowing through on its own without any help.
Once you've got the siphon flowing, you stick the round end deeply into the gravel and move it around, fairly vigorously. You''ll see all the dirt and goo come flying out of the gravel and get sucked up the tube and out into the bucket. It sucks the gravel up too, but because this is so much heavier, it just falls back down again. Work your way from one end of the tank to the other, making sure you have vacuumed every bit of gravel. Then simply lift it out when you're done. Because it removes water as well as dirt, the gravel vacuum usually forms part of your normal water change; you may need to remove only a little extra water afterwards to do your normal-sized change.
Gravel vacs are very clever things.