I imagine you're more interested in the political side of conquest instead of the logistical side I will use the first Greco-Persian war and the first Viking raids as back drops.

Let's begin with the first Greco-Persian war, while modern pop culture characterize the war as a simple Greece Vs Persia conflict. As in two distinct separate nations going at each other the truth is very different. While Persia(At this time the Achemenid empire), was a unified nation under a single imperial government its opponents were not unified in this sense. The Greeks were a people and culture not a unified nation. The Greeks were organized in various city states that while greek did not necessarily get along or have a common goal. These city states did share a common culture though and mostly saw themselves as part of the same peoples if not the same government. Think east and west Germany during the cold War. They were each distinct governments hostile to each other but were both parts of the idea of what it is to be German. So the Achemenid empire conquers each city state mostly independently one by one. Athens at that time forms a league of Greek city states and colonies (A city state may also have their own colonies which could and did grow to become independent city states) to fight the Achemenid empire on as a unified force. This however does not represent all of Greece or even the major powers of Greece. Various Greek city states were neutral and some were even allied to the Achemenid empire during its invasion of Greece. So thats how you get Athens and its Delian league fighting the Achemenid Empire all over Ionia while city states like sparta were simply neutral until the Achemenid empire threatened to swallow all of Greece into its empire. The Achemenid empire also had its own satelite states which while directed by them in the war, they were distinct and separate governmental entities (but thats the gist of that).

The idea of a couple of citizens arming themselves and invading a land to call their own while not representing their government is no where near ancient history. There have been attempts by the KKK to conquer Cuba that were foiled by the FBI, Utah began as its own distinct entity as the Mormons migrated west to found their own nation until the USA came west and absorbed them. The Norsemen were very similar to the Greeks in that they shared a common culture but not a unified government. The Vikings were not citizens of some kingdom that went rogue, the viking raids were organized by local warlords or rich men simply organizing an expedition by themselves. The unified nordic governments were actually born from these raids as the riches made some petty kings or earls stronger than others which inspired some to wage war on their neighbors as much as on the rest of Europe as raiders.

Conquest simply put is means of political change through the use of violence. Be it the Achemenid empire conquering city states, an Earl laying claim to an English village, or a mormon soldier fighting its first nation rivals for the creation of their own nation.