Viking settlements in Ireland developed organically from earlier raiding expeditions in the early 9th century. Settlements like Dubh Linn weren't originally established as nodes of military and political domination like you might see in other colonial contexts, but were founded as fortified ship encampments (called a longphort in Irish) that could allow raiding parties to winter on Irish soil rather than making a perilous winter-time journey back to Scandinavia and which developed over time into more centralized urban polities.

The creation of these proto-urban settlements was not really a concerted effort, and seem to have been undertaken on the initiative of independent raiding parties. Even immediately after their establishment, Scandinavian settlements in Ireland were targets of other Scandinavian raiding groups; the Annals of Ulster records that in 851 AD, only ten years after its creation, Dublin was actually sacked by a rival gang of Scandinavian raiders:

The dark heathens [Norwegians] came to Áth Cliath, made a great slaughter of the fair-haired foreigners [Danes], and plundered the naval encampment, both people and property.

In the early 860s some kind of royal authority was established over the settlement at Dublin by Imar and Amlaib, who are described in various Irish annals as the sons of the king of Norway (Amlaib's Irish epithet, Conung, is in fact a transliteration of the Old Norse konungr which means 'king') and who exacted tribute and subordination from most of the Scandinavian aristocracy in Ireland. Still, the Kingdom of Dublin wasn't really a colonial entity that was bent on pushing out the native Irish, and was more content trading with them, launching raids in Ireland and abroad and became just another player in the astoundingly complicated world of Irish politics and warfare.

Irish kings repeatedly sacked the settlement and drove out the Scandinavians, only to have them return several years later. In 902, a coalition of the kingdoms of Brega and the Laigin stormed Dublin and "the heathens were driven from Ireland, i.e. from the fortress of Áth Cliath... and they abandoned a good number of their ships, and escaped half dead after they had been wounded and broken." Those two Irish kingdoms sacked it again in 944, though the Annals of Ulster are clear that their intention was to carry off booty and treasures rather than to expel the foreigners.

The decline of the Scandinavian Kingdom of Dublin began in 980, when the King of Tara, Mael Sechnaill mac Domnall, inflicted a catastrophic defeat on them at the Battle of Tara and reduced their polity to a sort of tributary state for a short time. The Annals of Ulster state that Mael Sechnaill's victory resulted in the expulsion of foreign power in Ireland, which is more or less true because Scandinavian settlements increasingly became subjects of powerful Irish provincial kings, and were reduced to paying them tribute and supplying them with fleets and fighting men.