Sometimes it's obvious which sprinkler head is broken. In the worst case, you can see a spout of water coming out of the sprinkler head. Yet sometimes it isn't so obvious.
If you suspect you have a broken sprinkler head it's likely because a certain zone isn't working properly. So the first thing you can do is turn on that zone and determine which part of the zone isn't working. All of the sprinklers in a zone are connected in a line. So if you have one broken head somewhere in the line, all sprinkler heads before it will be working properly and the sprinkler heads after will either be off or have very low pressure.
Sometimes a broken sprinkler may not be easy to spot. There may be no immediate, visible sign of failure. Yet you might be able to hear it and you might be able to see a puddle begin to build up after a while. This is especially obvious when the sprinkler head is near a sidewalk or driveway.
Dig out around the sprinkler head. You will likely only need about 6-8 inches around the head. It's important that you don't dig into the pipe underneath the sprinkler so you'll want to dig carefully. You can use a shovel to break through the sod, but I recommend using a garden trowel to remove the dirt around the sprinkler head. You'll want to dig deep enough that you can see the main pipe underneath.
Oftentimes, there will be an riser between the main line and the sprinkler head. You can leave this in place as long as it isn't damaged. If the riser is damaged you can use a riser extractor to remove it.
The riser extractor is fairly simple to use. The fittings are shaped like a cone so you'll want to use the size that fits inside of the riser about half way. Press down hard and twist to unscrew. The extractor will catch the edge of the riser and turn it loose.
There are two important things to consider when finding a replacement sprinkler head - size and shape. The easiest thing to do is take your broken sprinkler head into your local Lowe's, Home Depot, or other hardware store and get help finding the correct replacement. Matching the size is fairly easy, but you'll want to pay attention to the shape as well. Common shapes are full circle, half circle, or quarter circle. As long as you take the broken sprinkler head it will be easy to match.
If your riser was broken you should also buy a cut-off riser. This will allow you to easily place your sprinkler head at the correct height.
If you need the replace the riser you can use the PVC pipe cutter to cut the cut-off riser to the correct height. Go ahead and screw the pipe into the sprinkler head first. Wrap the threads of the pipe with teflon tape before screwing it in. This will help prevent leakage.
If you didn't need to replace the riser or if a riser wasn't required, you can screw in the sprinkler head in exactly where you unscrewed the broken head.