This will be my first adventure in soldering, too. I went to my local thrift store and grabbed some cheap stuff to practice on. Even radio/alarm clocks have PBCs inside. Its good to note as you practice what condition you leave the bored in during soldering/desoldering since that is what you are worried about. If you don't have enough heat in about 2 seconds, let it cool and start over because you could damage the board. That is what I've been told.
Yes, you can damage the PCB, and lifting traces is common. Really, soldering/time only becomes an issue if you are soldering to a huge ground plane, which will absorb a lot of heat. If you have temperature control, heat up the iron more, and go quick.
I managed to lift a trace on an ALPS RK27 (potentiometer) breakout board, but I ended up just soldering directly to the pin anyway on that one.
Anyway, I'd recommend getting some sort of copper braid / solder sucker for mistakes, it really helps. There are some really good tutorials online for soldering. I liked the tangentsoft ones a lot:
http://tangentsoft.net/elec/movies/