I've made and finished cabinets for years and developed quite the knack for matching stains to various previously finished products or making wood components to match different plastic laminate wood grain colors.
My method wasn't very scientific, but it did work. It was just trial and error until you got the right match. The cabinet shop I worked at had 100's of colors of stains collected through out the years. I'd start with an empty can, find the color that matched closest, then i'd slowly add different colors until the blend was just right. I'd mix different brands as long as the base was the same, ie water or oil based stains, etc. The downside to this was, it wasn't a repeatable formula, but you usually ended up with plenty of extra to use down the road if needed. Just make sure you label the can!
Different finishing techniques also help match colors. Sometimes spraying a stain on works better than rubbing. Rubbing it on and leaving it for different periods of times before rubbing off, etc. Gel stains also seem to work great for matching existing products.