The best way to convince a skeptic of the benefits of meditation is to have them try it for themselves. A true skeptic may find it difficult to meditate however because it takes a certain amount of buy-in to be able to truly meditate. You may need to soften up a really skeptical friend about the benefits of meditation by having them read accounts of people who have benefitted even after being skeptical.
Once they are ready and willing to try, provide them with some pointers to help them be successful. Once they try it once, talk with them about their experiences and how they might change something in the future.