Some people would say that Isildur was already a great man long before he became a king, and thus he became a great king when he founded his kingdom. And of course founding a kingdom makes Isildur one of the greatest kings of that kingdom.
When Isildur was a young man, and merely the oldest grandson of Amandil, the last lord of Andúnië in the island Kingdom of Númenor, Sauron the Dark Lord, who had surrendered to King Ar-Pharazôn, was rapidly gaining control of Númenor, converting the king and the people to worship of Sauron's old master, Morgoth, the first Dark Lord.
Isildur feared that Sauron would soon have the sacred White Tree of Númenor destroyed. So Isildur managed to sneak past the guards and cut off a fruit from the White Tree and bring it back to his family, which became the ancestor of the White Tree of Gondor, even though he was severely wounded in a fight with the guards.
This story is told in The Akallabêth, the story of the Downfall of Númenor, published with the Silmarillion in the book called The Silmarillion, according to Ian Thompson's comment.
The Appendixes to The Return of the King have a lot of historical information. Appendix A, Annals of the Kings and Rulers, I The
Númenórean Kings, (i) NUMENOR, gives a brief history of the kingdom of Númenor during the Second Age of Middle-earth.
Appendix A, Annals of the Kings and Rulers, I The Númenórean Kings, (ii) THE REALMS IN EXILE, lists the kings of Arnor, heirs of Isildur, and the kings of Gondor, heirs of his younger brother Anárion.
Appendix A, Annals of the Kings and Rulers, I The Númenórean Kings, (iii), ERIADOR, ARNOR, AND THE HEIRS OF ISILDUR, gives a brief history of the region of Eriador, The Kingdom of Arnor, the three kingdoms that Arnor was later divided into, and the chieftains of the Dúnedain after the fall of the kingdoms, during the Third Age of Middle-earth.
Appendix A, Annals of the Kings and Rulers, I The Númenórean Kings, (iv), GONDOR, AND THE HEIRS OF ANARION, gives the history of Gondor when ruled by the kings, and when ruled by the ruling stewards, until the Return of the King.
Appendix B, THE TALE OF YEARS, has an introduction and then gives the chronology of The Second Age and then The Third Age.
In Second Age (SA) 3262: Sauron is taken prisoner to Númenór.
SA 3262-3310 Sauron seduces the king and corrupts the Númenóreans.
SA 3310 Ar-Pharazôn begins the building of the Great Armament.
SA 3319 Ar-Pharazôn assails Valinor. Downfall of Númenór. Elendil and his sons escape.
[Note the Downfall was the literal downfall of Númenór into the ocean. Elendil and his sons and the remnant of the Faithful of Númenór escaped in nine ships.]
SA 3320 Foundations of the Realms in Exile, Arnor and Gondor. The stones are divided (ii, 203). Sauron returns to Mordor.
[Note. Elendil was the King of Arnor, and the High King of both realms. Isildur and Anárion were the co kings of Gondor. Osgiliath was the capital of Gondor, and Minas Itil (later Minas Morgul) was Isildur's city and Minas Anor (later Minas Tirith) was Anárion's city. The stones were the palantiri. Sauron was killed in the Downfall, but his spirit returned to Middle-earth, carrying the One Ring, and Sauron made a new body for himself, black in color and very hot.]
SA 3429 Sauron attacks Gondor, takes Minas Ithil and burns the White Tree. Isildur escapes down Anduin and goes to Elendil in the North. Anárion defends Minas Anor and Osgiliath.
SA 3430 The Last Alliance of Elves and Men is formed.
[Note. Gil-galad was the last king of the Ñoldorin Elves in Middle-earth, and ruled in the west of Eriador.]
SA 3431 Gil-galad and Elendil march east to Imladris.
[Note. Imladris is the Elven name for Rivendell.]
SA 3434 The host of the Alliance crosses the Misty Mountains. Battle of Dagorlad and defeat of Sauron. Barad-dûr is besieged.
[Note. It is said that some members of every species of people, and of every type of birds and animals fought on each side at the Battle of Dagorlad, except that the Elves all fought for the Last Alliance.]
SA 3440 Anárion slain.
[Note. Anárion was hit in the head by a stone thrown from the Barad-dûr.]
SA 3441 Sauron overthrown by Gil-galad and Elendil, who perish. Isildur takes the One Ring. Sauron passes away and the Ringwraiths go into the shadows. The Second Age ends.
[Note. After being besieged for seven years, Sauron and a small group broke out from the Barad-dûr and headed for Mount Doom. Sauron's followers were all killed, and on the slopes of Mount Doom Gil-galad and Elendil fought Sauron, assisted by Cirdan, Elrond, and Isildur. Sauron was slain, but Elendil was killed and his sword Narsil broke under him as he fell. Gil-galad was burned to death by the black hand of Sauron, which was burning hot, perhaps when he tried to take the ring from it. Isildur cut the ring finger off of Sauron's hand to get the Ring. Círdan and Elrond advised Isildur to throw the Ring into the fires of Mount Doom, but Isildur kept it as recompense for the deaths of his father and brother.]
[Note. Sauron's spirit did not stir again in Middle-earth for about a thousand years, when it began encouraging evil creatures to attack. And it may have taken Sauron centuries or millennia more to create another body for himself, a body which lacked a ring finger.]
Third Age (TA)
TA 2 Isildur plants a seedling of the White Tree in Minas Anor. He delivers the south-kingdom to Meneldil. Disaster of the Gladden Fields, Isildur and his three elder sons are slain.
[Note. Meneldil was said to have been the last man born in Númenór before the Downfall, and so should have been about 124 years old by TA 2, and had watched his father Anárion be co king of Gondor for 109 years before Sauron attacked. It is possible that Meneldil didn't see any need for Isildur to instruct him how to be king. I can't help suspecting that Meneldil and Valandil were not as friendly to each other as they should have been and are largely responsible for the relative lack of cooperation between Arnor and Gondor.]
[Note. There is an account of the Gladden Fields disaster in Unfinished Tales of Númenór and Middle-earth]
TA 3 Othar brings the shards of Narsil to Imladris.
TA 10 Valandil becomes King of Arnor.
[Valandil was born at least as early as 3434 when his father Isildur left him behind in Imladris, and so was at least 17 in TA 10.]
As you can see, Isildur and Anárion landed in Gondor with their followers, persuaded the inhabitants there to accept them as their rulers, and founded the kingdom of Gondor, and built it up politically as well as building at least three cities and other infrastructure. And they ruled Gondor, under the authority of their father Elendil the High King, for 109 years until Sauron attacked. And both Isildur and Anárion fought heroically and led with skill during the war with Sauron.
So many persons would think that co founding the Kingdom of Gondor and ruling it for 109 years, plus heroic deeds rescuing a sapling of the White Tree in Númenór, and in the war with Sauron, combined to make Isildur a great king.
