We start with a given circle with center O, and a point P outside the circle.
Draw a straight line between the center O of the given circle and the given point P
Find the midpoint of this line by constructing the line's perpendicular bisector or my using scale.
Place the compasses on the midpoint just constructed, and set its width to the center O of the circle.
Without changing the width, draw an arc across the circle in the two possible places. These are the contact points J, K for the tangents.
Draw the two tangents lines from P through J and K.
Done. The two lines just drawn are tangential to the given circle and pass through P.