I have had several of my students ask me how to get backspin with their irons and/or their wedges. Backspin happens as a result of doing several things correctly. Here are a few tips:
1) You need to compress the ball at impact. To do this, good fundamentals like staying in your angles and in your posture will really help. Maintaining angles at impact and slightly into your follow through will allow you to get your bigger muscles into the shot.
2) Make sure your clubs are clean. Any dirt in your grooves will inhibit the spin you can get with your irons and wedges.
3) Overall, good technique and mechanics will help. Staying connected in the swing is really important because that is what will help you generate more power when everything is working together correctly. For help on staying connected, click on Staying Connected In The Golf Swing.
4) Make sure you are accelerating through the golf ball. You need to have some speed in order to create backspin and it's important to have speed at the right time in the swing which is through the impact zone. The club should gradually pick up speed so that it is traveling the fastest through impact.