In my experience, the easiest way to remove the old caps is to use two soldering pencils at one time. That way you do not put mechanical stress on the circuit board (as you do when you heat one side at a time). A grounded 15 watt soldering pencil is available from Radio Shack for under $10. So, if you already have one soldering pencil, go pick up a second one and make this job easy for yourself.
If you try to use just one pencil, by the time you can heat the second pad, the first will have cooled. With the one-pencil-method you are forced to either get the entire cap and board so hot that the solder will stay melted while you move the pencil from side to side, or you end up bending the cold solder on one side, while lifting the other side. That over-heating and/or bending is what typically leads to lifted pads on the circuit board.
With the two pencil method, you just apply a pencil to each end of the cap to be removed and wait until you can gently lift the cap with little to no resistance. It's useful to have a damp sponge on hand, as sometimes the cap sticks to one pencil tip or the other and it can be wiped off on the sponge.
