Declare, announce, publish, advertise, proclaim, promulgate, broadcast (and their corresponding nouns declaration, announcement, publication, advertisement, proclamation, promulgation, broadcasting) denote to make known (or a making known) openly or publicly.
To declare is to make known explicitly or plainly and usually in a formal manner.
To announce is to declare especially for the first time something presumed to be of interest or intended to satisfy curiosity.
To publish is to make public especially through the medium of print.
To advertise is to call public attention to by repeated or widely circulated statements. In its general sense it often connotes unpleasant publicity or extravagance in statement.
In its specific sense, as implying publicity for the sake of gaining patronage or support for an article of merchandise, it implies the use of communication media (as the press, the radio, handbills, or billboards); so used, it is devoid of unfavorable connotation.
To proclaim is to announce orally, sometimes by means of other sound (as of a trumpet), and loudly in a public place; by extension, to give wide publicity to, often insistently, proudly, boldly, or defiantly.
To promulgate is to make known to all concerned something that has binding force (as a law of the realm or a dogma of the church) or something for which adherents are sought (as a theory or doctrine).
To broadcast is to make known (as by radio or television) in all directions over a large area.