Question: “What is the proper way to use the beads, and what are the benefits?”
Chanting, of course, is a method of meditation. It gives you that focus and concentration on the words you’re saying, and by constantly hearing the words and furthering your understanding of them, a spark might go off and an “Aha!” moment might arise.
But the beads themselves have no power. Just like Buddhism as a whole is a tool, the beads are also a tool. A tool for what? Mainly for two things: to keep count and to help concentrate. We can either use the beads to keep count of the mantra we’re chanting or our breath. Some mantras have a special number associated with it (usually 3, 10, 21, or 108) – those numbers also do not have any “power” to them either, but different schools and traditions have their own explanation of the significance of the numbers.
The point of counting also, is to know when to come to a stopping point. Maybe we only have 5, 10, 15, or 20 minutes of free time, so we would only chant something for 3, 10, 21, or 108 times, depending on the length of the mantra. For example, I know that chanting “Om Mani Padme Hum” 108 times takes about 2-3 minutes at the speed I go, but chanting the compassion mantra for 21 times takes about 20 minutes. So the counting acts something like a clock.
Of course it also helps with our focus and concentration. By 1) focusing on the mantra, and 2) focusing on keeping count, it acts as a double shot of concentration. Of course, if the mantra is easily memorized or short, like om mani padme hum, then chanting and counting is effortless and some concentration will be lost by arising thoughts. Longer mantras or reading something new (or newish) will help keep the distractions away.
In some Esoteric Buddhist traditions, mostly in Vajrayana, using the beads in a certain hand, between certain fingers, and either pushing or pulling each bead has a specific “power” or characteristic – whether for healing, protection, wealth, etc., each way of using the beads supposedly opens up specific pathways and chakras for your intent. These pathways aren’t magical ways to cure sickness or make you rich, but again to give you concentration and determination to work hard to get well and be successful in your attempts of finding a new or better job, or some sort of funding.