First things first: the Hayes system uses DOT 3 or DOT 4 mechanical brake fluid. DO NOT USE MINERAL OIL FOR THESE BRAKES!!!!!!!
Second, the bleed starts from the caliper up to the brake lever.
Third, wear gloves.
You can get a bleed kit for this system so to prep your bike, you’re going to want to remove the caliper from the frame, remove the pads from the caliper and with the end of a 10mm box end wrench, push the pistons back into the caliper. Don’t push too far as you may break the post in the center of the piston.
You will need a bleed bottle to hang on the side you’ll be working on. In the video, they use a bottle and some zip ties to hang it on the handlebars.
On the caliper side, open the bleed port and attach your bottle filled with DOT fluid by using a box end wrench.
One important thing to note is that the reservoir on the handlebars (particularly in the Stroker and the El Camino models) are already at the highest point on the bike so there will be no need to rotate the reservoirs upwards. Wrap a rag around the area where the reservoir so that it catches any excess DOT fluid. If this gets on your frame, you may be looking at some considerable damage to your paint job or even worse, to your components.
You may want to remove both tires for this procedure.
Remove the bleed cap from the caliper and attach your bottle with the proper DOT fluid to the bleed port. You can secure it with a box end wrench. When all your bottles (and rag) are in place, open the bleed port by a quarter turn. With your bottle filled with new DOT fluid, squeeze liquid steadily into the system. And then release. Do that several times to make sure that you eliminate all the possible air bubbles trapped inside the caliper. Once you’ve done that, you can now give the bottle a good squeeze and get the fluid running through to the catch container.
Watch the tube of the catch container and be on the look-out for bubbles and the color of the fluid. Once it goes clear, you’ll know that you’ve pumped the system clean.
When that happens, you can close up the bleed port in the caliper and remove the bottle. Check to see if the pistons are still in their place with the box end wrench and go close the cap. If there is any excess fluid about, clean it off with alcohol and a clean rag.
Re-install your brake pads and make sure you don't get DOT fluid on them.
Mount your wheel and give your lever a good couple of squeezes. Get the fluid pumping through the system. You’re done!