The first steps to take with new data were already discussed in the previous post.
Factor analysis comes in two varieties: Exploratory and Confirmatory:
Exploratory factor analysis is used when you don’t have a clear idea of what items might belong together. There are many ways to see what items belong together. The principal component analysis is most commonly used. Items that hang together must also have face validity.
Confirmatory factor analysis is more complicated. This analysis tests that the hypothesized items belong to particular factors.