With your irons in hand the contact you are looking for is ball first, turf second. Many amateurs think the divot is created beneath the ball but this is a misconception, the divot should only start once you have struck the ball.
Here is a great drill designed to help you find the ideal angle of attack that leads to a ball first, turf second contact. Place a tee peg in the ground just in front of your ball as shown here. Take your normal address position but instead of focusing on striking the ball, concentrate on clipping the tee. If you have been struggling with your ball striking, this drill should help you find the right angle of attack with your irons.
If your ball striking is causing you problems, don't try to play through it. Book a lesson with your local Foremost Golf professional to get back on track as soon as possible.