The act created a mechanism for certain local officials to make a proclamation ordering the dispersal of any group of more than twelve people who were "unlawfully, riotously, and tumultuously assembled together". If the group failed to disperse within twenty minutes, then anyone remaining gathered was guilty of a felony without benefit of clergy, punishable by death.
The proclamation could be made in an incorporated town or city by the Mayor, Bailiffs or "other head officer", or a Justice of the Peace. Elsewhere it could be made by a Justice of the Peace or the Sheriff or Under-Sheriff. It had to be read out to the gathering concerned, and had to follow precise wording:
Our Sovereign Lord the King chargeth and commandeth all persons, being assembled, immediately to disperse themselves, and peaceably to depart to their habitations, or to their lawful business, upon the pains contained in the act made in the first year of King George, for preventing tumults and riotous assemblies. God Save the King.
Wikipedia has all this information and much more but, oddly, the link it gives to the full Act takes you to it via a website created by a bunch of fundamentalist nuts; if you want to study the Act’s 2,400 words it is better to get it from Project Gutenberg EBook. Its preamble is:
WHEREAS of late many rebellious riots and tumults have been in divers parts of this kingdom, to the disturbance of the publick peace, and the endangering of his Majesty's person and government, and the same are yet continued and fomented by persons disaffected to his Majesty, presuming so to do, for that the punishments provided by the laws now in being are not adequate to such heinous offences; and by such rioters his Majesty and his administration have been most maliciously and falsely traduced, with an intent to raise divisions, and to alienate the affections of the people from his Majesty therefore for the preventing and suppressing of such riots and tumults, and for the more speedy and effectual punishing the offenders therein; BE IT ENACTED…and so on, and on.
[In the United States the principle was incorporated into the first Militia Act of 1792. The act's title was "An act to provide for calling forth the Militia to execute the laws of the Union, suppress insurrections and repel invasions"; Section 3 gave power to the President to issue a proclamation to "command the insurgents to disperse, and retire peaceably to their respective abodes, within a limited time", and authorized him to use the militia if they failed to do so. Something similar is presently codified in Chapter 15 of title 10, United States Code.]