Multicore solder, correct temperature, clean then tin the iron first (to tin is to add just a little multicore solder to the iron): shouldn't be any problem soldering. Apply tip of tinned iron to joint for 0.5 to 1s then press solder against iron and pin simultaneously so it rapidly melts and flows all over joint, wait about 0.5s more, remove iron and solder, job done. It can help to trap the solder between iron and the pin being soldered (which means you didn't tin the iron!)
With tarnished copper, cleaning is often needed, but tinned or gold surfaces aren't a problem in my experience.