Well, the easy one is domestic courts. They decide whether a public authority has acted or omitted to act unlawfully under the Human Rights Act.
If the act is a decision about housing or immigration status or prisoners’ rights, the courts can quash it, and so tell the decision-maker either to decide it again or if there is only one lawful answer, tell the decision-maker what decision to take. If it was a past course of conduct (unlawful detention, intrusion into privacy, unacceptable pollution), they may award damages for human rights breaches. If the domestic law is itself unlawful, and cannot be interpreted HR-compliantly, the domestic courts can make a declaration of incompatibility under s.4 of HRA – it does the claimant no good in respect of his claim, though it throws a huge gauntlet down to Parliament to do something about the non-compliant law. And in the criminal courts, the obvious sanction is to dismiss the prosecution for some abuse of process involving the defendant’s human rights.