How do I change the rear tire on old Raleigh "Tourist" 3-speed Never changed the rear tire on this bike. How and what is loosened to remove the rear wheel so the tire can be changed?
This is where a 60 second Youtube  video is worth 1000 words. The adjustment takes less than a minute. There are a couple methods. If it is shifting ok now, mark the threaded rod where the cable attaches. Place the shifter in gear 3. Loosen the jam nut 1/4 turn, just enough to allow the cable end to unscrew from the threaded rod. with the cable disconnected, remove shifter chain guide nut. It may be separate or part of the axle nut. Remove the wheel as you would any other nutted axle. Reinstall the repaired wheel. You can reattach the cable screwing the cable end up to the jam nut. Tighten the jam nut. To check the adjustment. Place the shifter in 2nd gear. If you look at the shift chain guide you will notice two observation holes on the sides. If properly adjusted you should see about 1mm of the straight rod exposed. If more than 1mm is exposed loosen the jam nut on the cable end and expose a less of the threaded rod and tighten the jam nut. If less than 1mm is exposed loosen the jam nut and screw the cable end to expose less threaded rod.