I would recommend removing the old tiles first. I know this sound like a hassel, but the new tiles will adhere better. I've found that putting tile over tile tends to allow the tiles to slide. They work best when applied directly to an underlayment of some sort.
I've had the best luck removing tiles by heating them with a heat gun or blow-dryer to loosen the adhesive, then scraping off the floor. Once tiles are removed, there will be left over adhesive. Best thing I've found to remove that is tile adhesive remover -- found in any hardware store. Simply pain it on with a brush, wait the time, and wipe off. It's nasty stuff, but it will do the trick. Clean up with mineral spirits.