Details about Legolas family background are fairly sparse. The Prince of Mirkwood, though never once called by that (or any other title) in any of Tolkiens writings, is stated to be the son of Thranduil the Elven-king of The Hobbit. "There was also a strange Elf clad in green and brown, Legolas, a messenger from his father, Thranduil, the King of the Elves of Northern Mirkwood." (The Council of Elrond, The Fellowship of the Ring)  And on the Plains of Rohan, Aragorn introduced his Elven companion to Éomer simply as Legolas of the Woodland Realm, in distant Mirkwood. (The Riders of Rohan, The Two Towers) Appendix B of LOTR states that before the building of Barad-dûr many of the Sindar passed eastward, and some established realms in the forests far away, where their people were mostly Silvan Elves. Thranduil, king in the north of Greenwood the Great was one of these.

Much of the information we have concerning Legolas father Thranduil and grandfather Oropher comes from portions of essays published in Unfinished Tales. These sources often contain conflicting accounts and while some of it seems to be generally accepted, it is still open to interpretation and considered controversial.

According to the accounts in Unfinished Tales, Legolas family (at least on his fathers side) came from Doriath in Beleriand. Thranduil and Oropher were among the Sindar of Doriath who crossed the Misty Mountains and settled among the Silvan Elves there. Oropher is not mentioned in LOTR or its appendices. In one account these Sindarin adventurers are said to have wanted to blend with the Silvan Elves, adopting their language and lifestyle and taking Silvan names. This they did deliberately; for they came from Doriath after its ruin and had no desire to leave Middle-earth, nor to be merged with the other Sindar of Beleriand, dominated by the Noldorin Exiles for whom the folk of Doriath had no great love. They wished indeed to become Silvan folk and to return; as they said to the simple life natural to the Elves before the invitation of the Valar had disturbed it.  (UT: Appendix B, The Sindarin Princes of the Silvan Elves)

The Elven Princes name may or may not reflect this desire to merge with the Silvan Elves, though the name was established long before this essay was written. In Letter #211 (Letters) Tolkien states that Legolas means green-leaves, a woodland name dialectal form of pure Sindarin laegolas. And again in Letter #297, Legolas is translated Greenleaf (II 106, 154) a suitable name for a Woodland Elf, though one of royal and originally Sindarin line. Whether or not Oropher and Thranduil intentionally merged with the silvan culture, one could possibly interpret events to indicate that that is what eventually happened. For though Sindarin by descent (Elvish descent seems to be reckoned through the fathers line) Legolas embraced the culture of the Wood-elves and identified himself as Silvan.  That is true, said Legolas. But the Elves of this land were of a race strange to us of the silvan folk, and the trees and the grass do not now remember them.   (The Ring Goes South, FotR)

The quote from UT asserts that Oropher and those with him had adopted the language of the Silvan Elves. Elsewhere in the same essay Tolkien states that Thranduil, father of Legolas of the Nine Walkers was Sindarin and that tongue was used in his house, though not by all his folk. However, in UT: Appendix A, The Silvan Elves and their Speech, Tolkien tells us that By the end of the Third Age the Silvan tongues had probably ceased to be spoken in the two regions that had importance at the time of the War of the Ring: Lórien and the realm of Thranduil in northern Mirkwood. The continually evolving nature of Tolkiens mythology left behind many ambiguities, of course, and these conflicting statements regarding the status of Silvan Elvish cannot be reconciled. We can be certain though, regardless of whether or not the Silvan tongue continued to be spoken in Mirkwood, that the language of the Elves of Third Age Middle-earth was Sindarin. In Appendix F of LOTR it is stated that Sindarin was the tongue of all those Elves and Elf-lords that appear in this history. For these were all of Eldarin race, even where the folk that they ruled were of the lesser kindreds.

Being a Sindarin prince Legolas would undoubtedly have been quite well educated, however, it is improbable that he knew Quenya given the attitude of his grandfather towards the Noldor. The use of Quenya had been banned thousands of years earlier and had long since become a language of lore. The Noldorin Exiles adopted Sindarin as their daily language and even in Lórien Sindarin had become the language of all the people.   (Unfinished Tales, Appendix B, The Sindarin Princes of the Silvan Elves)

So we can conclude that Sindarin would have been Legolas native tongue, possibly along with Silvan. He was clearly proficient in the Common Speech (Westron). He may also have known the language of the people of Dale, as their own language was still in daily use and the Wood-elves likely had dealings with them long before Westron spread that far east (according to The Appendix on Languages found in Peoples of Middle-earth, HoME XII). My guess is that he probably would have known little if any Quenya.

Again drawing from the essays in UT, the folk of Thranduils Realm are said to have long ago migrated from the south, being related to and once dwelling near the Elves of Lórien. In LOTR, when welcoming the Fellowship, Celeborn greets Legolas as a kinsman, so it would seem that Thranduil and Celeborn, both originally from Doriath, could possibly have been related. "Welcome, son of Thranduil! Too seldom do my kindred journey hither from the North." (The Mirror of Galadriel, FotR) It is also possible that the kinship he speaks of refers to their common Elvish or Sindarin heritage rather than any actual familial relationship. It would seem that by the time of the War of the Ring Thranduils people had put their prejudices in their past, or perhaps the Woodland prince did not share his elders views, as Legolas seemed thrilled upon the occasion of his first visit to Lórien.

Returning to UT: Appendix B as a source, we read that during the Second Age Oropher resented the intrusions of Celeborn and Galadriel into Lórien and the power and proximity of the Dwarves of Moria. Therefore, he began to move his people northward through Eryn Galen, the Great Greenwood; the immense forest which was their home. After Sauron moved into the southern part of the forest (About TA 1000) Oropher continued to move north, until eventually, under Thranduil, the Elves settled in the far northeast corner, establishing his stronghold in a cave system after the manner of Thingols Menegroth.  

Family and age:
We have no information at all concerning Legolas mother or whether or not the prince had any siblings. Nor do we know when he was born. Thranduil (presumably with Oropher) established his realm in Greenwood the Great before the year 1000 of the Second Age (Appendix B, LOTR). So, the Elven-king would be at least 5460 at the end of the Third Age. Unless Legolas came with them from Doriath, he was probably born somewhere in Mirkwood. That Legolas is not mentioned as having been present at the Battle of the Last Alliance lends support (but no proof) to the theory that he was born sometime in the Third Age. There is no way to know.

Many readers notice Legolas exuberance, playful attitudes and curiosity and surmise that he must be relatively young (for an Elf) and there is reasoning to support that theory. Michael Martinez, in his article, Speaking of Legolas, hypothesizes that if Legolas had been born near the end of the Watchful Peace (TA 2063 2460) that could explain both his youthful behavior and his limited travel experience. A birth date of TA 2460 would make him 559 in TA 3019. However, Legolas himself makes several comments in LOTR that indicate that he does not consider himself to be young at least not while in the company of the Fellowship. Of Fangorn Forest he says, It is old, very old, said the Elf. So old that almost I feel young again, as I have not felt since I have journeyed with you children. It is old and full of memory. I could have been happy here, if I had come in days of peace.     (The White Rider, The Two Towers)  And when riding among the Huorns he comments, "These are the strangest trees that ever I saw", he said; "and I have seen many an oak grow from acorn to ruinous age. I wish there were leisure now to walk among them; they have voices, and in time I might come to understand their thought."     (The Road to Isengard, The Two Towers)  

Oak trees can have an average life span of as much as 700 hundred years, indicating that Legolas would probably be somewhat older than that. On the other hand, his remarks could very well mean that he has seen thousands of years go past. However, if one prefers the young Legolas theory consider this: possibly for Legolas, spending an extended amount of time in the presence of so many mortals may have simply accentuated his sense of age, prompting comments that he would not have made had he been among his own people. It certainly caused him to ponder the contrast between elven and mortal perspectives and elvish perceptions of the passage of time. Legolas stirred in his boat. Nay, time does not tarry ever, he said; but change and growth is not in all things and places alike. For the Elves the world moves, and it moves both very swift and very slow. Swift, because they themselves change little, and all else fleets by: it is a grief to them. Slow, because they do not count the running years, not for themselves. The passing seasons are but ripples in the long long stream. Yet beneath the Sun all things must wear to an end at last.   (The Great River, FotR)

In my opinion his remarks indicate that even if Legolas is not particularly old for an Elf, neither is he exceptionally young. Living 800 years would leave its mark on a person, even if he were considered young compared to others of his kind. He assuredly felt the weight of age when among his mortal companions. Yet a comment like Five hundred times have the red leaves fallen in Mirkwood in my home since then, said Legolas, and but a little while does that seem to us.    (The King of the Golden Hall, The Two Towers) could suggest as much a reflection of elvish perspective as personal experience. Though he might have lived in Mirkwood longer than the Rohirrim had dwelt in Rohan, he may have acutely perceived the paradox if he was still considered young by other Elves. But, again, there is far too little evidence to come to any decisive conclusion.