If it's dried roots, enclose them in some cheesecloth or something similar, tied up, and cover with water in a pot. If powdered, you can tie them up in some coffee filters. (Use a pot you don't care about, and something you don't need to cook in ever again... once you do this, it can no longer be used for cooking.)
Cover so that the water is just past the top of the bags. If you want to maintain a reddish dye, this will be a bit tricky, because madder can't be heated too quickly or too hot. Start on low, and gradually increase the temperature up to medium. Let this simmer for about a half hour, and use an object to drop a droplet of the liquid on a paper towel. If it's a deep color, then it's ready to drain. If still a bit thin, let it simmer more. You want the concentrated color from the bottom. When ready to drain, pour it out, re-fill the pot and repeat this until you have enough dye extracted for what you'd like to use.
Note that if you want a brown shade from the madder you can increase the temperature to medium high, or high. Madder being boiled gets the browns to come out.
Once you have the dye extracted, add a bit of the original dried madder to the bunch and allow it to ferment, which will result in a really rich dye, but it will take about four months. If you do this, keep the mixture in a jar or corked bottle so you can burp it regularly. Glass is inert, so it won't interfere with the process.
The fermented dye will need to be strained, and can be applied with a sponge, brush, etc. Once applied it's a good idea to buff the area lightly to remove excess dye on the surface, then oil the skin. This forces it to dry from the inside out, rather than the outside. If it dries from the outside, you'll lose color as it does. I recommend adding about 10% to the volume of the dye you're using some galnut extract, as this is the best anti-UV agent I've found, and a pinch of soda ash and citric acid (quite literally a tiny pinch). This helps to saturate the leather collagen. Don't worry, the effect on the leather will be negligible. All the dyes I make test to be near neutral pH. The soda raises the pH so that you can add the pinch of citric acid in the least damaging pH range.
You can follow this process for other substantial dyestuffs, such as barks, walnuts, beat roots... fruit you can also ferment, though without boiling. Just crush the stuff a bit and ferment, again for about four months. Some require longer due to climate, so test when you think it's ready. Generally it's ready when it smells of cheap wine.