Homo-Neanderthalis were in the general area, but they were pushed out by Cro-Magnons. Homo Sapiens Sapiens showed up maybe 35000 years ago, but there was little to distinguish them from their predecessors. About 1200 BC, waves (or at least wavelets) of migrations arrived from all directions, and that may have set up the divisions of Italy's "prehistoric" tribes. Somebody moved onto Tiber Island about then, but nobody really knows who it was. Within 200 years, that is by 1000 BC, there were huts on the Palatine and Capitoline Hills, and those on the Palatine had coalesced into a village by the middle of the 8th century BC.
Romulus, the first "King" of Rome, ruled that 8th century Palatine hut settlement, according to legend. The Roman historian Livy (Titus Livius) wrote up the history of Rome's seven kings 500 years later. The seven Roman kings, Livy said, were:
Romulus ("a Roman") -- 753 to 715 BC
Numa Pompilius (Sabine)-- 715 to 672
Tullus Hostilius (Sabine) -- 672 to 641
Ancus Marcius (Latin?)-- 641 to 615
Lucius Tarquinius Priscus (Etruscan) -- 616 to 578
Servius Tarquinius Tullius (Etruscanized Greek)-- 578 to 534 and
Tarquinius Superbus (Etruscan) -- 534 to 510 BC
In 510 BC the last King, a brutal tyrant, was deposed and the Roman republic was founded in 509 BC.
Livy's history ran to 142 volumes and, as luck would have it, the first volume, which briefly covered the 243 year period of the Roman monarchy, is one of the 35 volumes that weren't lost. The average reign of the kings, by Livy's accounting, would have been just shy of 34 and three-quarters years.
Livy clearly had earlier sources for his summary history of the Roman monarchy, but nobody knows precisely what all of them were. He picked and chose what he considered to be the most plausible stories and then constructed a linear account, which he presented as the factual history of Rome's kings.
Modern historians think Livy combined traditional stories about the names of kings and the legendary lengths of their reigns and that he then simply counted backwards to arrive at 753 BC as date when Romulus founded the city of Rome. The traditional lengths of their reigns are extremely unlikely -- the just don't square with life-expectancies of the time -- but there may be more truth to their names and the approximate times of the start of their reigns.
Start with the names: The name of the first king, Romulus, is most often interpreted as meaning simply "a Roman" (as in "Rome was founded by a Roman"). The names of subsequent Kings are not drawn from the extremely short list of names used by Roman families. In fact, they are drawn mostly from name lists of other local peoples, mostly Sabines and Etruscans, and that argues in favor of their credibility: Livy certainly didn't hesitate to weave into later volumes the names of powerful Roman families of his time, during the reign of Augustus, that wanted to be memorialized. If Livy and his unknown predecessors had just made up "traditional" names for the kings, they would undoubtedly have chosen good "Roman" names rather than names used by people who had become conquered enemies in the intervening years.
Although the lengths of reigns attributed to the seven named kings are unlikely, the timing of the starts of their supposed reigns are somewhat plausible: they vaguely parallel the ups and downs of the fortunes of local groups (especially the Sabines and Etruscans) before they were all totally eclipsed by the "Romans" during the monarchic period or during the early years of the Republic. Livy refers to some short interregnum periods between the reigns of the kings, and they and other similar periods between kings could partially account for the overlong reigns ascribed to the named kings. Some historians believe that there may have been short-lived dynasties -- families whose members had the same or similar names -- which legends and traditions compressed down into singular kings.
Livy was a prestigious writer, and he had the patronage of Augustus, so nobody in his own time was likely to question his historical judgement too closely. Later historians and even some of our own near-contemporaries have just accepted what Livy wrote. Many more modern historians accept the reigns and actions of the kings as just another part of Roman mythology, but they add that most myths have some basis in fact.
So if the stories about the kings and what they did aren't really true, why do they matter? Even if the myths fall short of "truth", they were an important element of the ancient Roman belief structure, especially during earlier periods of ancient Rome. Even in periods when explicit belief in the historicity of the kings had wavered, the monarchic myths provided apt pedagogic models of approved and disapproved Roman behavior. Roman kids were drilled with the deeds and misdeeds of the kings and of the folks that finally removed them and set up the Republic. Those traditional lessons were transmitted by later Roman historians and again by Franklin, Locke, and Montesquieu in the 18th century and the "lessons learned" were woven into many of today's republican constitutions.
Getting the "lessons learned" up to modern times: http://www.mmdtkw.org/VPolybius.html
Chronology from the Forum Romanum web site:
Founding of Rome, Romulus and Remus: http://www.geocities.com/~stilicho/romulus.html
Numa Pompilius, Tullus Hostilius, and Ancus Martius: http://www.geocities.com/~stilicho/numa.html
Tarquinius Priscus, Servius Tullius, and Tarquinius Superbus: http://www.geocities.com/~stilicho/tarquin.html
Livy's history, the first volume -- from Troy through the kings: http://etext.lib.virginia.edu/etcbin/toccer-new?id=Liv1His&images=images/modeng&data=/texts/english/modeng/parsed&tag=public&part=1&division=div1
Modern scholarship on the kings -- Mackay, UAlberta:
http://www.ualberta.ca/~csmackay/CLASS_365/Early.Kings.html, and http://www.ualberta.ca/~csmackay/CLASS_365/Later.Kings.html