So if you find yourself in my friends position, what you need to do is to simply give up on these solder pads. Any further heating or abuse could lead to the traces coming up and affecting solder pads near by.
To carry out the work-around you need to follow the traces under the board (the lines that are slightly raised from the surface of the PCB) to another solder pad and solder to that. Simple.
If these were through-hole components with legs that needed soldered to (and the solder pads are now unusable), first clear the holes of the solder pads by heating with a soldering iron on one side of the PCB and using the desolder pump on the other side. With the holes now clear, place the component through and solder a wire from the leg to the alternative soldering position.
When you understand how PCBs and electrical connections work, this work around seems extremely obvious. However, I know it's a stress that many people starting out in electronics have experienced so I felt it was a worthwhile topic to post on.
- Use (high-grade, fast flow) leaded solder
- Remember the "heat on one side of the PCB, desolder pump on the other" trick to clear solder from inside a pad.
- Use a decent metal desolder pump.
- Don't get worked up! If it's frustrating you, take a break, stare at kittens on the internet for a while, then come back to it.
- Read-up on how PCBs work and deepen your understanding of electrical connections.
And finally, please always remember: Don't Panic! It's very rare you've truly destroyed your DIY electronics project. There are always more components and decades of troubleshooting that have led to plenty of workarounds.
What would you add to this advice?
UPDATE: Joe Vezzetti on the DIY Audio Facebook group pointed out you can get electric desolder guns that heat up like a soldering iron. you place them over the pad you want to desolder then press the button and BAM, you're done. Here is a model he has suggested (although he notes they start around $500).
Cheaper versions can be found online, but as with all DIY tools, you normally get what you pay for.
Another option that occurs to me now is using the heat gun from a reflow station (normally used for SMT work).