Dwarfholds mentioned:

Thunder Gorge, in the northwest of Denning (Northriver province) - destination of Pack of Sevenhills.

Sevenhills, home hold of Pack.

Gulfport, current home of distinguished dwarves who complain to Victory about Gnome Day.

Finestone, home hold of Leverage (original boss at the Clever Man's Works).

Golden Mountain, home hold of Escapement, Craft Master of the Jewelers and Devicers.

Ironrock, home hold of Loadbearing, Craft Master of the Engineers and Metalsmiths.

Copperhills, home hold of Deal, Craft Master of the Traders and Logisticers.

Red Hills, home hold of Sublimation, Craft Master of the Substancers and Mages.

Double Peak, near Mount Morin, home of Torsion and Sprocket.

Coppercast, not far to the east of Old Koslinmouth. The Coppercast dwarves are New Dwarves.

Prospectors go out, and where they see certain signs that indicate valuable ground, they talk to the landowner and to the Localgold and get a license to investigate further, with an option to buy the land for its value as farmland—plus a bonus, if the potential of the place is realized. Then they dig a test pit, and see what the subsoil and the rock are like, and what minerals there are.
If they decide to proceed, they call in their option to buy the land, and bring in their relatives, and dig. And once the hold is established, it is a free city, beholden to nobody, self-governing.
(However, the dwarfhold is taxed to maintain the roads that ship their products out.)

The Gnome Party wants to found gnomeholds along the same lines as dwarfholds and with similar privileges.