Congratulations, you must have a situation that is just right for your orchid. It looks like a phalaenopsis. In nature the second plant would start rooting in the same medium that the parent is rooting in.
The no-risk solution is to get another pot with the same medium (looks like bark chips from the photo) and plant your latest addition into it. Wait until you can see that the leaves and roots of the new plant are growing and cut the link to the parent.
If you are willing to take a little more care of the baby orchid you can cut the link now and pot it up. The roots that you see are more for mechanical attachment than drawing nutrients. The preferred day temperature for Phalaenopsis orchids is 75-85 deg F(24 - 29 deg C) with a lower night temperature. Do not let the medium stay wet. Soggy rooting medium causes rot. If you can increase the humidity and air movement for your new plant this will help new growth.
EDIT: If you cut the roots now then you should make sure the new plant has the best conditions possible such as higher humidity, warmer temperatures, bright but diffuse light.
If you pot the new plant up and leave it attached then you don't have to do anything more than wait until it is larger and better established.