Getting your core to engage under load is a must when lifting weights. Practicing the deadbug is one of my favourite ways to teach your body to activate the correct muscles under load. This exercise also helps to reinforce proper breathing patterns and diaphragm breathing.
To do this exercise you will need to breath out and draw your stomach in while lowering each limb. Inhale and expand the stomach as you bring the arm or leg back up to the top. The video shows me moving one arm and leg but if this is too challenging you can start with only lowering an arm or just one leg.
You may progress this exercise by adding a stability ball. Push your knees and hands into the ball while you perform the exercise.