Probably 2 types of pipes you are dealing with.
PVC pipe
Funny pipe. Yes, that’s what it is called.
You will have to start digging at the head and follow the funny pipe back to the pvc by digging.
Usually the installation has PVC running through your yard with Funny Pipe running off the PVC which allows easier placement of sprinkler head since the Funny Pipe is flexible.
You can dig around the head, and use this fitting to connect a new piece of Funny Pipe to the existing Funny Pipe and run it to wherever you want to place the head.
Attached FileI have relocated heads, and added heads to existing zones by using combinations of the fittings in the picture above plus Funny Pipe.
Here is a picture that probably resembles what you have underground.
Attached FileYou can buy all these fittings at Home Depot or Lowe’s.
FYI... Your sprinkler heads are probably running a 1/2” fitting and 1/2” Funny Pipe. Home Depot and Lowe’s sell the 1/2” Funny Pipe.
Attached FileThis is really a VERY SIMPLE DIY project. If you pop a hole in your existing Funny Pipe then it’s no big deal, just cut it below the puncture and add a new piece with the fitting above.
I have found the easiest thing to cut the Funny Pipe with is PVC cutters. You can do it with a knife but it probably won’t be a really straight cut.