I've done it many times, but not recently so memory is a little fuzzy.
Don't recall if you have to take the indicator needle and dial plate off, but it sure makes it easier. If you do, press the needle stop peg in--it's spring-loaded--and let the needle rest in a normal position (vertical). Note the position of the needle--that's your speed calibration. The needle can be carefully pulled off--if it seems stuck then leave it on lest you break it. You'll need a jeweler's screwdriver from one of the little kits to remove the two small screws holding the dial plate on.
The tripmeter reset rod is spring-loaded too, as you probably know. You'll need to push it up as you try to finagle the internal mechanism out. IIRC, it's easier if you remove the bulb holder for the high beam light. It has a tube that goes to the plastic 'jewel' that encapsulates the light from the bulb and makes it more difficult to maneuver the internal mechanism. The bulb holder has two small, copper clips that hold it in the case; carefully press them inward and pull the bulb holder and tube out. It will have a small length of a rubbery tube that makes the final connection between the bulb holder tube and the 'jewel,' it'll either come out with the tube or stay affixed to the 'jewel' or fall off (it's probably very brittle by now).
The rod is two-part; if you still have the bottom part--that would usually hold the knob--you need to remove it to shorten the rod. It should have a tiny roll pin you can push out (think I use one of the jeweler's screwdrivers for a drift).
It's mostly a matter of getting just the right angle on the mechanism and pushing the rod in. If the speedo hasn't been disturbed, there will be a thin metal washer (maybe two), a felt washer and a spring--that's about the size and shape of a ball-point pen's spring--under the rod spring that is used to seal around the rod's hole. Note the arrangement and be careful not to lose them.
BTW, if it's only the bottom section of the rod that is broken you can replace it--see my comment on tiny roll pin--without removing the mechanism from the case. If you need to replace the entire shaft I can't tell you much as I haven't done it, but there will be a way. Remember, these devices were assembled by hand, so can be disassembled as well.
Edit: Substitute 'lens' for 'jewel'