How to solder wires to terminals depends on the type of wire and type of terminals.
There are two kinds of insulated wires: solid wires and stranded wires.
In any case, the wire must be stripped of its insulation before soldering to the terminal.
The most popular in the USA
Weller WE1010 solder station
Hakko FX-888D soldering station
Weller WLC100 (cheap solder iron)