Hi and Welcome! I use a shovel called a 'sharpshooter' (long narrow blade)to dig down to the pipe, I used to use a regular ole smokey the bear round nose but it makes a big hole in comparision. Take caution not to get dirt or debris in the pipe while you are removing the failed head. Then wrap the threase with new pipe tape to minimize leaks at the connection. Then all you need to do is adjust in the new one (radius, arc, gpm nozzle, ect...) and you are ready to go.

I have tried with a pressurized water hose, it helps to dig up a hole quite nicely, but watch out the the dirt that flies up to your face.

Once the dirt is roughly removed from around the head, I use a dandelion weeding fork to do the fine digging.

If your problem is just with the internal parts of the head - I have simply removed a small amount of earth with a trowel, screwed out the sprinkler 'innards', replaced part as necessary and screwed it back in. You end up discarding the body that you scavenged parts from but saved a bunch of digging.