I think the right way to do it is to pull the rear wheel off of the bike and let the air out of the tire.
Then, one side of the tire would be broken loose from the rim and pried off so the inner tube can be removed.
The rim tape that covers the heads of the spoke nuts should be pushed to the side in the area of the broken spoke so you can remove the spoke nut.
Then, it's just a matter of looking at the other spokes to make sure how they are positioned, position your new spoke in a similar matter and screw the spoke nut on.
Tighten the spoke nut until the spoke "rings" like the other spokes.
While your at it, tap the other spokes with a screwdriver blade to make sure they all "ring" the same (or nearly the same). None of the spokes should go "doink" or sound like they are "dead". That indicates it is loose.
If they don't ring about the same pitch, adjust their tightness.
Put the rim tape back in place along with the inner tube and the tire bead.
Fill the tire with air and reinstall the wheel.
While your buying a replacement spoke you probably would be wise to also buy new rim tape.
http://nfieldgear.com/enfield-store/aftermarket-parts-accessories/tires/rim-tape.htmlThe rim tape often gets weathered, cracked and stuck in place and it's the only thing that keeps your inner tube from chaffing against the heads of the spoke nuts.
A backup inner tube would also be a good idea because there is a very good chance of you poking a hole thru your existing tube while your are trying to pry off the tire bead (or pry it back on).
Based on my last experience in prying off a tire, plan on using the whole day.
Good luck.
The cheap non advisable way of doing this task is to let the air out of the tire.
Twist the broken spokes nut gently back and forth to break it free from the rim tape.
Insert the new spoke into the hub.
Move the spoke nut slightly inward towards the inner tube while you try to align the threaded end of the spoke with the nuts threads. Gently bending the spoke a bit may help.
Once the spoke nut screws onto the spoke easily (do not force it), it can be tightened to the proper tension.
OK you guys. Feel free to jump on me.