The sons of Elendil, Isildur and Anárion, upon arriving in Pelargir did set about building the watchtowers of Minas Anor and Minas Ithil, and between them their great city of Osgiliath. Alas, it was not to be long before Sauron rose again and was defeated in the Last Alliance, but with the loss of Anárion in SA 3440 before Barad Dur. Isildur it was who cut the one ring from Sauron's hand, but it betrayed him, costing his life to orcs in TA 2.
In the days of the eighth king, Gondor was first attacked by Easterlings, who were driven out. The king took the name Rómendacil (East-Victor) in celebration. The twelfth king, Tarannon Falastur, expanded the navies of Gondor and conquered the coasts to the west and south. He was the first of the four Ship-Kings. His nephew Eärnil it was who first conquered Umbar, haven of the Black Númenóreans, followers of Sauron. However, in the next reign Umbar was lost.
The fifteenth king, whom history calls Hyarmendacil (South-Victor), led Gondor to its greatest expanse. It was he who destroyed the navies of Umbar and forced its kings to pay homage to Gondor. He extended Gondor north to the Celebrant and the southern eaves of Mirkwood, west to the Greyflood, east to the Sea of Rhûn and south along the coasts to Umbar. Yet his sons did grow lax and so evil came to Gondor.
The second Rómendacil cared deeply for his allies,the Northmen of Rhovanion, and so did send his son Valacar to live among them. This prince married a woman of the north, although many Gondorians felt she was inferior. Their son, Eldacar, was beseiged in Osgiliath but evaded the usurper Castamir who ruled only a short while (and showing his great cruelty in the process) before Eldacar returned to kill him at the Crossings of the Erui. Castamir's sons did flee to Pelargir and thence to Umbar which was lost to Gondor. And this was the great Kin-Strife.
In the reign of Telemnar a great plague struck which did kill the king and all his children and a great many others of Osgiliath. With him died the White Tree brought from Numenor by Anarion. After him, during the reign of Telumehtar, Gondor again took Umbar, but it was soon to be lost forever.
When the Wainriders attacked a third time, Gondor could just manage to hold them to Ithilien, which was destroyed. In this battle was lost Ondoher, king, and his two sons. The crown passed to Eärnil, captain of the Southern Army.
Eärnil was followed by one king only, Eärnur. He it was who wished to challenge the Witch King at the fall of Angmar, yet was restrained by the Noldor Glorfindel. However, the Witch King did not forget the rash Gondorian king, and later challenged him to single combat. In this time, the Dark One's forces had taken Minas Ithil, which they re-named Minas Morgul, and in response had Eärnur called Minas Anor, Minas Tirith 'Tower of the Guard'. Eärnur rode out to meet the Witch King's challenge, disappearing into Minas Morgul with all his companions.
His Steward, Mardil, ruled Gondor for many years, the watch passing down through his house to the current Steward, Denethor, the crown remaining in the lap of King Earnil in the Houses of the Dead, where Eärner had placed it.
The map of Gondor (click for a larger image)
The map of Middle Earth (click for a larger image)