The balance is the heart of the watch, together with the hairspring it is the component that makes the movement keep time.
To remove the balance you must first remove the balance cock, to do so first remove the screw then place the blade of a screwdriver into the notch at the back of the cock and with a twisting motion carefully pry the balance cock away from it’s seat on the pillar plate. Then to remove the balance from the cock you must turn the whole assembly upside down and lay it flat on the bench, then loosen the hairspring stud screw and carefully lift the balance complete off the cock, some movements have one regulator pin that is bent at it’s end or made to cover the hairspring and keep it from coming out of the pins, for this type you must turn the regulator pin away so the hairspring can be lifted out of the regulator pins.
To remove the hairspring from the balance slide a small thin screwdriver blade under the collet at the notch and carefully twist the screwdriver side to side until the collet is free from it’s seat. A hairspring collet tool can also be used, you wedge this into the notch in the collet and with a twisting motion pull the collet up and off it’s seat.