How do you write validation rules with ISCHANGED, PRIORVALUE, and ISNEW? How do you bypass a validation rule for certain users?

ISNEW() returns true when the record is being created (not on updates). Use it to enforce required-on-create conditions.
ISCHANGED(field) returns true if the field value changed during an update. Example: prevent changing the Status from "Closed" back to "Open":
ISCHANGED(Status__c) && PRIORVALUE(Status__c) = "Closed"
PRIORVALUE(field) returns the previous value of a field before the current edit — only meaningful in update context. Combine with ISCHANGED for targeted change validation.
Cross-object validation: Reference parent record fields using the lookup relationship syntax in validation rules.
Bypassing for specific users:
— Use $Profile.Name = "System Administrator" or a custom permission: $Permission.Bypass_Validation_Rules in the validation rule formula with a leading NOT(...) or as a condition to short-circuit evaluation.
— Error placement: set the error to a specific field for inline display, or "Top of Page" for a general message.