The benefits of recovery days are huge. When you work out, you can get microtears in muscles. Microtears can add up over time and lead to a sprain or strain. You also want to manage inflammation; when you acutely work a muscle, it secretes lactic acid. The longer the lactic acid stays [in your muscles], the longer it can irritate the muscle. If you're getting microtears, we want to heal those as fast as we can.
As for how often to take a recovery day, once a week is normally enough unless you're intensively training. If you're doing hugely intensive workouts, you may need a two- to three-day recovery period. You can also rotate muscle groups — for instance, one day you work the upper body, the next time you do the lower body. This can give you a longer recovery period.
The most important part of a recovery day is hydration, hydration, hydration! You can't move anything out of your cells if you're not well hydrated. A good healthy diet with proteins, fruits, and veggies is important, as is sleep. When you do harder workouts, you need more sleep.
On recovery days, working on your flexibility and stretching can have highly beneficial effects. I also recommend avoiding alcohol, especially after a stressful or acute workout, as it can increase inflammation.
As for supplements to take to complement your workout and recovery routine, I love Magnesium. It supports muscle relaxation and healthy muscle function.* The Office of Dietary Supplements reports that 48% of Americans are not meeting their daily requirements for magnesium, so if you aren't eating lots of leafy green veggies, legumes, whole grains, nuts, and seeds, you may want to supplement.
Another great way to treat your body on a recovery day is Epsom salt soaks! Epsom salt is made from magnesium, so it can help relax your muscles as you soak. Plus, what's better than a bath?