Go for an iron with temperature control and a fine, chisel tip. There are many good brands, Weller is market leader, but cheaper irons can work well too. The chisel tip adds more surface area for more heat conduction.
Flux is very important. No good soldering happens without Flux. Also important to keep a clean tip. I recommend tinning the wire or the contact pad and tinning the iron tip. This should give you enough solder to make the joint without having to hold a piece of solder.
I love Cardas Audio Quad-Enteric solder https://www.cardas.com/supplies Super low melting point makes it great for electronics parts that might be damaged by too much heat.
