Contract your back muscles throughout the exercise. On a chin-up, pull your shoulders back and down, then start the lift. Look skyward, and try to pull your sternum up to the bar. At the top, hold for a few seconds, then lower yourself to the bottom without losing the contraction.
Build up in reps with assistance, then your body-weight, then begin adding weight (either by holding a dumbbell between your feet as you hang, or by wearing a belt with a chain for attaching plates/dumbbells). This will take you several weeks to month(s), to be able to lift the extra weights as many as 10 in a row.
Rush nothing, be deliberate with no swinging. Count 3 seconds up, hang for 2 seconds, lower for 4.
On alternative days, do cable rows, holding your back in the same posture. Count with the same frequency. If you can do 10 reps or more, increase the weight.
On alternative weeks, change to pull-down machine, but with your legs pinned, do not make the exercise focus on moving the weight but on trying to push your sternum up to the bar. As it lowers to your chest, hold your contraction.