A designation is an administrative act, not a court judgment. An authority decides that a person or entity meets the criteria in a legal instrument, and publishes that decision.
What a designation entry actually contains
It is a structured record rather than a sentence of prose: the primary name, known aliases, addresses, dates and places of birth or incorporation, identity document numbers, and the programme tag explaining why the party is listed.
Those identifier fields are what screening systems match against, which is the whole reason so much evasion effort goes into supplying a counterparty identity that is real, verifiable and not on the list.
What happens on publication
The restrictions attach immediately. Property is blocked or frozen, dealings are prohibited, and any institution holding relevant property must report it.
There is generally no grace period, though authorities frequently issue a wind-down general licence permitting the orderly termination of existing business within a stated window. The scope and expiry of that licence is one of the more common subjects of penalty notices, because parties continue relying on one after it has lapsed.
Getting off a list
Delisting processes exist in every regime and are used. In the United States a party petitions OFAC; in the EU there is an annual review and recourse to the Court of Justice; at the UN there is a focal point and, for one regime, an Ombudsperson.
Delistings are published in the same feeds as designations, which is why the designations feed on this site records both.