(I am self-taught so my method may vary from the orthodox.)
There is no need to remove a solid tire from the rim to install new spokes. There is no air tube to puncture.
-place nipple wrench on the nipple of the broken spoke
-turn the broken spoke to unscrew it from the nipple
-run the new spoke through the proper hole in the hub, and bring the threaded end to the nipple
-bend the spoke just enough to insert the threaded end into the nipple
-with nipple wrench turn the nipple to tighten the spoke
true the wheel as necessary. See my thread "Truing the bicycle wheel"