Shortly after occupying Egypt, Alexander the Great decided to found a city. A dream - or so Plutarch says - led him to the site: an isthmus near the Canopic mouth of the Nile, where a small island created a sheltered harbor. Once he had decided on the location, Alexander ordered his architects to outline the walls and streets of the new city. Since no chalk was at hand, the king impulsively ordered barley from his supply train to be used instead. (Plutarch goes on to note that the barley was immediately devoured by birds, whereupon Alexander's quick-thinking soothsayers assured the king that this was an omen of future prosperity.)

Picturesque? Yes. Apocryphal? Quite possibly. But Plutarch's account of the foundation of Alexandria - soon to become the greatest of all Hellenistic cities - is based in the actual processes of city-foundation.

Before discussing the foundations of Alexander and his successors, it might be useful to comment on the phenomenon of Greek colonization. "Colonization" is an unfortunate term, since it evokes the very different aims and attributes of both Roman colonization and the successive waves of European colonization in the modern era. Very briefly, from the eighth century BCE onward, many Greek cities sent out parties of settlers to establish new poleis. These parties were motivated by a complex of goals - the push of overpopulation and restricted social opportunity, the pull of commercial promise, etc. - but they had this in common: the cities they founded, whatever their actual ethnic composition (settlers frequently intermarried with local populations), were little islets of Hellenism: socially, politically, and culturally Greek.

Greek colonies were seldom just clones of the mother city, and often evolved along very different political lines (see the tyrannies of Sicily and the experiments of the Pythagoreans at Croton). They were independent, often defiantly so, of the cities of old Greece. But they continued to be part of the Greek world, sending athletes to the Olympics, suppliants to Delphi, and the occasional philosopher to Athens.

Enough about the phenomenon; you want to know about the actual process of city-foundation. There are a few literary descriptions - the most famous is Herodotus' account of the establishment of Cyrene - but these tell us next to nothing about the apportionment of land and construction of buildings. Archaeology is more eloquent, showing evidence in many Greek colonies of equally-sized lots - apparently given to each citizen-colonist - and rectilinear streets designed to ease the process of land apportionment. To judge from this evidence, new Greek cities were, from a very early date, "planned" - outlined in advance, with locations chosen for an agora, the primary streets, and walls. Though not a colony in the strict sense, the neat plan of Priene (a foundation of the fourth century BCE) is an impressive witness to the methods of such planning.

Alexander and his successors were heirs to both the tradition of Greek colonization and the conventions of Greek city-planning (as refined by Hippodamus of Miletus and his followers). They applied both with gusto to the challenge of creating a network of Greek cities in the vast new territories of the Hellenistic world.

As in the original epoch of Greek colonization, the motivations of Hellenistic city-foundation were mixed. Security was often the paramount consideration, since the kings saw cities filled with Greeks - often veterans of their armies - as guarantors of regional stability. Commercial advantage was another factor; Alexandria in Egypt was only the first of many Hellenistic cities placed at a strategic node in the local trade routes. It used to be claimed that Alexander and his successors also hoped to "Hellenize" their domains, but most modern scholars regard this as unlikely.

Though not established as part of some grand plan of acculturation, the new Hellenistic cities were thoroughly Greek in their institutions and dominant culture, even when many or most of their inhabitants were non-Greek. The most spectacular example is Ai-Khanoum in northern Afghanistan, probably one of Alexander's foundations (which I discuss in an older answer). Here, more than a thousand miles from old Greece, the settlers established a polis with an agora, temple of Zeus, and gymnasium (where the Delphic maxims were proudly inscribed).

As in the case of pre-Hellenistic colonization, archaeology is more helpful than literary sources in determining how cities were founded. Typically, it seems, the king simply granted a civic territory to a group of settlers, provided them with various financial incentives (often some combination of initial tax breaks and discharge bonuses for time-expired soldiers), and - perhaps - a few surveyors to facilitate the division of the city site and surrounding territory into private lots. This much seems clear from the surviving remains of cities like Ai-Khanoum, where straight streets and (initially) equal urban lots suggest a careful initial land distribution. Private enterprise did the rest.