It depends what your research questions are, and how many variables you have. For 2 variables and a research question stressing "association" it's a simple spearman correlation. For multiple IVs and one DV you'll need more complicated regression (gneral linear) models of your preference (e.g. multinomial regression with dummy coded predictors. For multiple IVs and multiple DVs you'll need Structural Equation Modelling.
For two ordinal variables, one test of association is the "linear-by-linear test". The data are arranged in a contingency table. I think SPSS produces this test automatically in some of the chi-square output. I think it's called "lxl" in the output. A reference for the test is Alan Agresti, An Introduction to Categorical Data Analysis, 2nd ed.
Why not correlate the ratings for the variables using Pearson's r? The Linear by linear association essentially does this as it is:
(N-1) * r^2
where N is cases and r is Pearson's r. Quicker and easier than using a contingency table and also quite possible to to switch to say Kendall's tau or Spearman's rho.
Alternatively an ordinal approach such as logistic regression ... but there isn't much value to anything beyond a r or rho here.
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