Seek out independent research.
The FDA puts the onus on supplement manufacturers to do efficacy testing on their products so that they can make health claims about them. Sometimes companies will conduct decent, well-designed trials to show that their products work. More often, though, these studies are pretty weak — like, for example, a trial of 10 guys ages 18 to 70 who took either a supplement or a placebo for one week. Studies like that don't prove much of anything, so always take statements like "scientifically proven" or "backed by research" with a giant grain of salt.
Usually, the most credible science is independent research done on specific ingredients that their products contain. For instance, a university study that linked niacin to lower heart attack risk, or a meta-analysis that found that St. John's wort combats mild depression. Even though findings about specific ingredients don't always translate to a finished supplement's contents, they can give you a better indication that a product will work. If you're considering trying a new supplement, look past any marketing hype, and do a little research of your own to see if there are studies to back the ingredients in the product.