You can buy desolder braid at any electronics store, it is basically a copper strand that when heated ontop of solder absorbs it and removes it from the solder point.
You can also use a desolder bulb by heating up solder and depressing and letting go.
If you think the removal will be painfull, you may wish to just use soldering iron on all points and slide up the pin header, look between all pins and make sure no bridges and try powering, by heating up solder you may bring any solder bridges out by pulling soldering iron up the end of pin header and leaving excess on pin.
1st attempt at soldering, could be a # issues not related to your skills. 1st verify using electronic solder and not plumbers solder. Also, when wires appear soldered try pulling on wire and see if secure or loose.