How do I solder this tiny QFN chip
Short answer: You can't with your equipment.

That's a .5 mm (20 mil) QFN.  Trying to solder that with a soldering iron will only make a mess.  Ideally you use solder paste, a stencil, accurate automated placement, and a reflow oven.

I have soldered similar chips with a hot air station and some care.  Use a soldering iron to put a bead of solder on all the pads.  You want the amount of solder on each pad to be as even as possible, but there should be a clear "bulge" of solder on each pad.

Then liberally apply paste flux and very carefully place the chip correctly over the pads.  Use a magifying light or similar to make sure the chip is aligned close to right.  It doesn't have to be exact, but you don't want any part of a pin over a adjacent pad.  This step is tricky, especially since it's hard to move the chip the tiny amounts required for final alignment.

Next apply hot air.  I usually use around 700&deg;F, but only the minimum air flow you need.  Try to heat the chip as evenly as possible.  After a few seconds, you will see the solder melt, at least on one side, then hopefully all sides a second or two later.  At that point the surface tension of the molten solder will align the chip nicely.  You will probably see it move.  Leave heat on for another few seconds just to make sure everything is really melted, then remove heat and let cool.  This whole step should take maybe 10 seconds, 20 tops.