Also, once you've scraped your trace (all the methods Fredrow describe will work), I also like to 'prep' the traces before I try to attach the wire:
Apply a dab of paste flux to the trace. I recommend "no clean" flux, as you can use rubbing alcohol to clean up "no clean" flux.
Use your soldering iron and solder and apply solder directly to the trace.
Clean up the flux (I use q-tip and rubbing alcohol).
Apply a second coat of fresh flux.
Now, put some solder on your soldering iron and then try to attach the wire to the trace.
Clean up the flux again.
"Prepping" the trace (for me, anyways) makes it easier to attach the wire. And flux just makes everything easier. It may sound like a pain in the ass to apply two coats of flux and have to clean each time, but I guarantee that this is faster way to go. We do hundreds of installs every month and using this method actually SAVES us time and increases the quality of the connections. Also, I like to lay the wire parallel with the trace. For example, I scrape off 3-4 mm of the trace, then strip the wire back about 3-4 mm, and then try to lay the wire right down on top of the trace parallel to it. This gives you more surface area for the wire to stick to the trace. If you use this method, you'll make a GOOD SOLID connection between your wire and the trace, so be CAREFUL not to tug hard at the wire - you'll rip the copper trace right off the board!
Also, we use 30 gauge wire. I wouldn't use anything larger.