A few ways to go about it.
If that picture is of a pencil type soldering iron, its too small to do a good job.
40 watts? I think is minimum.
Iron hot,touch wire and hit iron tip with solder where its touching wire. It should take solder,and follow the running solder as it wicks up the wire.
Flux paste,heat wire and dip into flux,a couple times. Wiping wire off each time.
I use my utility knife to scrape wire after stripping,before twisting.
If wire is dark at all, its better to use solderless crimp on terminals.and use heat shrink, the double wall stuff.
I use a butane powered soldering pencil. Good tool, but they wear out. About 5 years is all i get out of them. Snap on or mac.
Next time will be a weller.
