Before you dig, it's a great idea to call Dig Alert.
Set up an appointment with them and have them come in and mark the existing utilities. Just in case you run into an old pipe. It's safe to know that there's a utility present and not assume it's just an old abandoned pipe.
Once that is done, proceed in digging around carefully enough making space to work around broken clay pipe, and clean loose debris.
Make a deep pothole 14 inches long x 14 inches wide x and 12 inches deep, right in the center below the cracked pipe, so that when you open the clay pipe...the dirty water or sewer gray water goes down below the pipe in the deep pothole and prevent yourself from getting your feet dirty.
Cut the roots that caused the break in the first place and or remove palm tree if necessary to prevent future sewer breaks.
Dig into the dirt back a few inches away from the broken section, and leave enough space to measure and cut that clay pipe and install pvc sdr 35 or ABS sewer black pipe same outside diameter (O.D.)
Never glue parts in other projects and assume its going in perfectly.
Always dry fit first, so you have an idea of how all dry fittings will fit.
Never gun it, without knowing how the actual connections may fit, or make the mistake in cutting without measuring the pipe to short.
Or not having enough pipe to do another cut, or do a second run to the hardware store and it's getting dark.
Grab your measuring tape and measure the end of one side to the center of the no hub stainless steel bands coupling rubber fittings, transfer those measurements to the ABS or SRD 35 pvc pipe and to the previously square cut clay pipe.
Check pitch fall with level and make sure all marks align with the rubber couplings, then ...torque to specs.
Let the water run for a bit and and check for leaks.
After all is checked OK! Backfill 12,14 inches with clean damp sand and carefully compact around the pipe little by little. Then the rest of the dirt can be covered with clean soil compact it to top of grade and leave a few inches to put the green turf back how it was.
Always make a note and take measurements where the crack happened and make a small drawing or sketch for the near future, in case of replacing the whole sewer or making other repairs to the sewer system.
Very simple job! There's nothing to it!
Best regards Juan
Good luck! :)