I am trying to create a table for an assignment on normalization. It is similar to the problem here : http://pubs.logicalexpressions.com/Pub0009/LPMArticle.asp?ID=88

I am trying to make it so that if a name appears in the Spouse, Child 1,2 or 3 column it will automatically appear in a dependants database with the EmpID and the Name of the Dependants, as separate objects so that the EmpID could be repeated. I have scoured info and I can't seem to make it work. Any help would be appreciated.

Your description of your table structure is definitely not normalised. All people are people so you should only have one table. A junction table should then perform a self join on this table indicating the nature of the relationship.