I created a file geodatabase with some tables. I created a new table and specified the field properties. Now, how do I open the table to populate the fields?
You open the table in ArcMap by adding the table or layer to the table of contents, right click on the layer and select open attribute table (if it's a table look for it in data view). Then you can use field calculator or edit the cells individually by clicking in them and entering data.
One more important thing, to edit cells in a table you must be editing, field calculator does not require you to be editing but gives an extra level of undo (the normal undo and you can always not save the edits).
Look at this page http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//005s00000038000000 for nice pictures and covering topics I have skipped over.