There are two types of follow-up tests: planned contrasts (when you have hypothesised specific group comparisions) and post hoc tests (when you haven't hypothesised specific differences - tests all pairs of groups).
To learn more about conducting follow-up tests for ANOVA, consult:
For a factorial ANOVA, if you get a significant F for an IV which has more then 2 groups and you had made no hypotheses, then your main options are to followup with post-hoc tests, choosing among:
In order to get these analyses:
You only need to report one set of post-hoc analyses.
Once you get the results, interpretation is pretty straightforward, because you will have a series of comparison tests between each pair of means, showing either significant or non-significant differences.