I was able to fix my tent pole with the existing elastic cord since only the last 3 inches of the cord was broken. My poles have a rounded end on one side, if yours are the same use pliers to twist this plastic piece off.
Make sure there is a knot at the end large enough to prevent the cord from being pulled through the opening. I was able to carefully guide the cord through each piece of the pole without using anything to help guide it through. If you are having difficulty doing this, tape your cord to some wire that is thin and stiff enough to guide the cord through. You could even try a bamboo skewer. Thread the cord one piece of the pole at a time. Make sure that the poles are facing the correct direction so they nest into each other. Once through, nest the pole into the previously threaded piece.
Use your toe or even better a clothespin to hold the cord to prevent it from snapping back through the poles and losing all your work.
Once the elastic is through all the poles tie a double or triple knot. Make sure you leave some stretching room so the poles can be folded.