Not sure I understand your question. Are you asking how to solder the wires to the PCB?

The picture looks like the PCB of the Rio remote; how did you crack it open? Is it still possible to re-assemble back to original? (I'd hate to screw up my remote...)

I'd say scrape a bit of the laquer off that covers the PCB and track,clean and then solder onto the tracks. You want to be very careful, as it may well be possible for the tracks to come loose; potentially rendering the entire thing useless.