In my experience it is not really worth it to try and construct your own egg ring. They are very affordable as it is and you will not really save that much money if you purchase the supplies and assemble one yourself. However if you have some of the appropriate tools and resources it can certainly be done for no cost at all and may be worth the effort if money is tight. In the following I will provide some suggestions for construction if you choose the DIY (do it yourself) route.
The first and most important component to construct is the ring that will sit on the surface of the pan. The best metal for this that most people may have around the house is definitely aluminum. Aluminum is a very malleable metal and can also withstand the heat from cooking. It will be the easiest to form into a ring shape (if it is not already) and it is durable at the same time. Aluminum foil will be much too flimsy, so look for a thicker aluminum in your basement or storage area. Most duct work for heating and cooling systems is aluminum so check to see if there are any scraps around that you could use.
The second aspect to construct is the handle for managing the egg ring. This can be made from any long, slender object that you have around the house. However keep in mind that it is helpful is your egg ring is dishwasher appropriate so make sure it is a durable material and is not a hard cardboard or anything else that will wear down in the dishwasher.
Finally, you will need to connect the handle and the metal ring. This sounds like a very simple task, but you need to make sure that the handle will not get too hot to touch. If you end up using metal for the handle you will need some kind of buffer to prevent heat from traveling up through the handle. This can be done in a number of ways, but if we are trying to keep the price at $0.00 than I would recommend a small piece of wood fastened in between the two pieces. Obviously if your handle is wood than you do not need to bother but if not than I would recommend just cutting a very small square to use out of anything available. I should note that even if your handle is made of wood it can still get very hot and you may need to wrap it with Styrofoam (or something similar) that could be removed for cleaning.
Hopefully this helps all you do it yourselfers out there that are always trying to save a few bucks. Happy cooking!