well… depends. the hardcore, by-the-book way of doing this would demand for you to factor-analyze the polychoric (or probably polyserial, depends on your data) correlation matrrix. SPSS wont do that for you by itself. you either need to use an SEM-specialized software (the AMOS extension in case you’re using SPSS, EQS, Mplus, etc.), my beloved R (which is free and can be downloaded) or i’m pretty sure someone out there must have coded some sort of SPSS macro on the internet that you can download and use for free.
nevertheless, if your likert scales have enough points, you can probably get away from doing it with the Pearson correlations in SPSS like you would do in any other case. in my very own and biased experience doing my own monte carlo simulations, once you get to 5-point likert-type scales, whether you use the polychoric correlation matrix (the right way of doing it) or the Pearson’s correlation matrix doesnt create too much of a difference. if you get to 7- points the differences are so minimal that you can really just analyze the data as if it were regular, continuous data (ONLY in the case of EXPLORATORY factor analysis. for CONFIRMATORY factor analysis things get more complicated)