I solder TQFP-44 parts (PIC 18F46K22) with pretty good success. You'll need a fine tip solder iron, flux, and a decent magnifying glass (unless your eyes are good enough).
1) Apply flux to the pads.
2) While the flux is still wet, place the part on the pads. You don't have to have it in the correct orientation yet. You are just putting flux on the leads.
3) Orient the part to the correct position.
4) Start in one corner and align the pins so they are centered on the pads in that corner, both X and Y.
5) Tack solder ONE leg only. There should be enough solder from the PCB tinning to not require adding any at this time.
6) Repeat the process on the diagonal corner.
7) Re-inspect the first corner and adjust if needed.
8) Start soldering the un-tacked side of the part. I'm right handed and found going from left to right minimizes solder shorts.
9) Solder all remaining pins.
10) Inspect for shorts. If some are found, apply more flux and use a fine solder wick. Press down on the pads (not into the pins). The solder on pin shorts will wick down to the pads as pad solder is removed.
11) Have patience!