You can basically create one table defining surrogate key. For example if you have tables like
Region
(idRegion
RegionName
)
and
Country
(idCountry
idRegion
CountryName)
if your composite key in Country is idRegion and CountryName then you can create a dim table as
dimCountry
(idCountry
RegionName
CountryName)
where idCountry will be your surrogate key in the dimension table.