Sounds like you're describing a keiki. Leave it on the parent plant until it develops a few roots and then you can cut it from the parent plant.
Pictures of the plant in question would help to further confirm that the orchid, in fact, does have a keiki growing. I'm assuming you have a phalaenopsis as its usually the most commonly purchased among first time growers.
Yes, pictures would help. If it is a kei kei on the stem just let it grow until the roots are about 4 inches long or so, then cut it off and pot like a regular orchid. Viola! New orchid that will bloom just like its parent.