This exact same chip was my first replacement job of soldering/desoldering on a PCB - i was a bit nervous, but in the end its pretty easy.
Snip the legs off the top side of the existing IC, then with your soldering iron heat up the "legs" that are left in the holes and use a little $12 solder sucker thingo from jaycar to clean the holes out and remove the legs.
Give that area of the board a quick clean
Solder a socket in (this is where you take a deep breath, relax and maybe use a magnifying glass)
Push the new IC into the socket
Done!!