You will also want to get a flux pen, a desoldering braid, a sponge, and a continuity tester or multimeter capable of continuity testing.
The soldering iron you use is a very crucial part. Even the most experienced solderer will have problems if the iron is crap. So hopefully the one you have is fine enough. Also having a precision tip on it helps immensely, especially when dealing with multiple wires next to each other.
For practice you should solder on whatever spare board you can find with the chip with the smallest pins you can find. Clean the pins with a qtip dipped in alcohol and mark the pins you are aiming for (not necessary for the flexpcb install but should you have to revert to the wire install it will help). This will help you a LOT as your eyes can go blurry easily when looking at all the pins so close together. A fine tipped felt marker is good for this job. Then flux the pins with the pen (don't worry about getting flux on other pins since only the heated pin will bind with the solder). Clean your iron every now and then as needed -- when it loses the shine on the tip. To do this wipe it on the sponge and then apply a thin coat of solder to the tip. Solder without a rosin core is better for this since there won't be any rosin to burn but you can use rosin core if that's all you have. Tin the wire you are going to attach to the pin with a thin layer of solder -- not a blob! Also tinning the pin on the chip helps a lot but it can be difficult to do properly if you don't have extremely fine solder. Then put the wire in place, steady your hand, and heat the pin and the wire at the same time to (hopefully) bond them together for good. Keep the wire in place for a couple of seconds until the solder is totally solidified so you don't make a cold solder joint! Then give the wire a little tug to make sure it is solid. If it comes loose then you might want to clean up any excess solder still left on the pin if it looks dull; retin the wire and try again. When you think you have a good connection then do a continuity test on the pin and the other end of the wire. Then check for continuity on the pins on either side and the end of the wire (getting continuity would be bad here). If you have bridged pins then the first thing to do is not freak out. Freaking out can make things get very bad very fast. Just get out your desoldering braid and clean up the pins. Then test the continuity of the pins and make sure the bridge is gone. Then try to solder the wire again. You should mess up your test subject (spare board) on purpose by bridging some pins together and unbridging them. It will boost your confidence in being able to correct an error if it should arise during the install and let you know that you aren't totally screwed should you bridge some pins together.
That's about all I can think of. Good luck on the install
