I've done this repair 2 or 3 times.
Requires removing instrument cluster
Also requires a new "button" from Volvo dealer, about $2-3 or so.
It's acutally L-shaped, and the "L" breaks into 2 legs.

1) pop off the panels on left and right sides of cluster, remove 1 screw at each corner of cluster. Pull part way out of dash.
2) carefully remove wire connections at rear of cluster & note which goes where.
3) note that red & white wire is ONLY used if you have a tach, otherwise it fries lots of stuff real quickly!
4) pull out cluster the rest of the way
5) remove 7 screws holding circuit board assembly to rear of cluster assembly
[One screw at each corner, the others along the long edgess]
5) remove screws (4?) holding down the speedomoter
6) pull off speedometer
7) now you can replace the broken plunger stick
8) You'll see it works against a spring, I think it's sort of a flat-blade spring. I bent mine back some to require LESS pressure to reset the odometer. I'm convinced that the spring was designed w/too much tension, needing a hard push on the reset button, so it breaks.
9) Reassemble carefully. Outer, visible end of reset button drops into hole in cluster from the rear.

Remember to stay away from the red and white wire.