You've been told that your worst putt will probably be better than your best chip, so you putt when you can. And most of the time when you chip, you still want the ball to roll more like a putt. But sometimes you need to play a chip shot that checks up quickly, perhaps because there's danger if the ball rolls too far. For those times, you need a chip shot that spins.
Choose the right club. It's much easier to get backspin with a lot of loft. Your most-lofted wedge is usually your best choice but don't be afraid to experiment. You may find that you get more backspin with your sand or pitching wedge than a lob wedge because you make better contact with the ball. Sand wedges and pitching wedges have taller faces than a lob wedge, so you're less likely to slide completely beneath the ball.
Address the ball correctly. Most players prefer to open their stance slightly, with no more than 8 or 9 inches between their feet, and put a bit more weight on their forward leg. This helps ensure that the shaft leans forward and helps you deliver a descending strike on the ball. However, you don't want to put the ball too far back in your stance as doing so can keep you from hitting the back of the ball cleanly. A good rule of thumb is to let your arms hang down and imagine a line dropping straight down to the ground from your hands. Place the ball between that spot and the inside of your back foot.
Hinge your wrists slightly on the backswing. Think "hinge," not "cock." You don't want a lot of wrist cock, just a little flexibility in the wrists as you reach the end of your backswing. This hinging will let you get a bit more "oomph" on the ball without swinging hard. A smooth stroke will make it easier to get solid contact on the ball.
Trap, don't dig. You don't want the club head to take a big divot when you chip. The club head should brush the ground, but you don't want it to hit hard enough to stop the club. You're not trying to make the ball check and spin back toward you. You just want it to roll forward less than normal.
Keep a firm left wrist at the finish. The shaft and your left forearm should still form a straight line at the end of the stroke. If your wrist is "breaking down," it's a sign that you've stopped turning your shoulders before you finish your stroke.