I grew this particular plant from seed - planted in March, it grew on a windowsill with some help from a lamp until the weather got warm.
I moved it into a bigger pot that is currently on our deck. The only downside of keeping it outdoors is that it does seem to serve double-duty as a snack for our cats and for whoever wanders by at night.
Like many other herbs, catnip will flower and you want to make sure to pick the flowers off or trim it back.
Considering how much this sells for in pet stores, and considering that it is much stronger when fresh, it has been very worthwhile for us to keep a catnip plant on hand. We have had no complaints.