Cufflinks can be worn with either single cuffs, which look just like a regular buttoning dress shirt’s cuffs but with holes on both sides of the opening, or with doubled-back “French” cuffs. French cuffs will have two holes on either side of the opening, which should line up one atop the other when you fold the cuff back.
To fasten the cuff, the holes on both side of the cuff opening are lined up, the cufflink is inserted through so that the post runs all the way through all the holes, and the link is then set into its closed position.
The sides of the cuff are most commonly matched up “kissing,” with the interior faces touching one another. This turns the hemmed edges of the cuff opening outward from the wrist, one atop the other.
It is not “wrong,” however, to fasten the cuff sides overlapping rather than kissing. In that arrangement, the underside of one edge of the cuff lays atop the outer face of the other edge, so that only one hemmed edge points outward.
The overlapping or “barrel” style looks more slim and business-like than the more ornamental “kissing” look. Neither are wrong, but the kissing approach has traditionally been considered better suited to the ornamental nature of cufflinks.