You need to know the difference between defining a projection and actually projecting a feature class.
If you have a feature class in which you have no projection information, you need to go back to the data source to find out what projection the data is in and then DEFINE PROJECTION as such.
Once you have a feature class with (correct) projection information and you want to present that data in a different projection, you will run the PROJECT tool.
That should just about do it....