Identify the cord diameter for replacement.
On cheap tents this will usually be around 2mm in diameter which is not very strong or durable.
If you measure the opening diameter of the pole you may find you can use a thicker diameter.
On my tent poles I went for a 3mm diameter cord over the existing 2mm.
You can purchase the cord on ebay. I am in the UK and got 10 meters for around £3.
Note, The new cord (3mm) is black in the photos and the worn old cord is white with blue and red.
You will need a minimum of 10 meters for a two man dome style tent which has two tent poles. Any tent bigger than two man dome you will need to measure the pole lengths assembled and purchase length accordingly.
Update: I recently measured the original cord and found it to be 50% of the length of the poles when assembled.
So depending on the amount of elastic stretch in your cord, you could purchase a new cord that was 75% of the length of the assembled poles as a rough guess.
You now need to find yourself a threader to feed the cord through.I have found an excellent metal threader inside an old windscreen wiper. So when you come to replace your windscreen wipers save them Or salvage some from your local garage.You will find two strips of metal which run the length of the wiper blade you need to remove these from the wiper blade assembly.The best wiper blades are those from a saloon car or a van for the best length.Ideally you need wiper blades of length around 50cm - 52 cm so they are just longer than a single pole of the tent pole assembly.Note, my photo shows a windscreen wiper but its too short also NOT ALL WINDSCREEN WIPERS have metal inserts.The cheaper wiper blades are unlikely to have metal inserts.
You now need to join the threader to the new cord.This is done by a butt joint of the threader and cord together and then securing with a very small amount of sticky tape. I used one revolution of sticky tape here in the photo.Do not use a lot of tape as this will add drag to the threader and make it stick to inside wall of the tent pole.