Usually, you create a shapefile (or other feature class) by either creating the features first – polygons, points, lines, etc. – then, creating attribute fileds (table columns), and then filling in the attributes (there are different ways to do this – directly in the table is one way).
Or, if you want to plug some existing attributes that you already have (say, in an Excel table) to an existing shapefile, you have to make sure that at least one field (column) in both the shapefile and the new table has exactly the same attributes; and then you use the “Join” command.
But it seems like you are interested in creating an attribute table for a shapefile (or other geographic feature class) which doesn’t exist yet. That’s unusual for GIS, but I’m sure it happens. Sounds like you already found a way to do it – “New Table” – but it’s not working the way you want it to. Well, I’m sorry I’m not helping you much with that specific issue, but at least maybe I’m helping you put your stated workplan in the context of how things are more commonly done.
The one time I often create a table all by itself before a shapefile exists in in the case of GPS points. You generate a table by taking points with your GPS, entering attributes in one or more columns (either “in the field”, or back on your computer, using Excel or maybe the GPS’ own software). Then, you convert these into a point shapefile in ArcGIS, using the “Add XY features” command. At least, I think that’s what it’s called. It used to be that this would create a temporary “event” file (stupid name for it – it always made me think of trying to park near a stadium for a rock concert or something!), which you then had to “export” as a permanent point shapefile. That process may have changed in 10.0.