They're not adjusted. If you devise orthogonal planned contrast, then you don't need to adjust your p-values because this would be equivalent to partitioning your data so that each contrast involves nonredundant pieces of information. This is why orthogonal planned contrasts can be so beneficial! Normally, with orthogonal contrasts, one wouldn't be interested in the omnibus F test, but it's interesting to note that summing the sum of squares of all your orthogonal contrasts will add up to the sum of squares between of the omnibus ANOVA. This makes sense because it confirms the notion that one is partitioning the sum of squares between into a series of nonredundant tests.
If your planned comparisons are not orthogonal, then you do have to adjust your p-values and there are many alternatives for doing so. It's hard to recommend a specific approach without knowing more about your design. Some approaches are more conservative than others (e.g., Bonferroni), but you can also look into Dunn's test or Scheffe's tests.