We first meet Legolas at the council of Elrond in which he is there on behalf of the Elven kingdom of Mirkwood.
He tells the council that Gollum has escaped from his kinsmen's guard and, though they tried to find him, they failed as he traveled into what used to be known as Greenwood.

*SIDE NOTE* This area was where Legolas was originally born but, due to the influence of Sauron, it became a dark place overrun by hideous huge spiders of Shelob's making.

Elrond chooses him to go on the quest with the others and he thus becomes a member of the fellowship. As they travel, Legolas' skills with his bow and arrow prove useful as he downs many wolves during the long nights. He even manages to see the crebine which threaten to expose the fellowship.
After a dangerous trek up the mountains, Legolas leaves the group to "find the sun" in which he discovers an easier way to get back down the mountain as they had kinda been snowed in.
When they reached the Mines of Moria, Legolas commented on the fact that Dwarf doors are invisible, saying that it didn't suprise him that their own masters could not find the openings.
When a huge tenticle monster attacks Frodo, it is Legolas who shoots one of the tenticles off and then proceeds to blast it right in the eye with an arrow.
Once inside, there is some peace but, since Elves hate confinded spaces, Legolas was a bit uneasy. When a huge fight breaks out, it is Legolas who can shot off two arrows at the same time, both finding their mark, and who ultimately kills the attacking cave troll.
The fellowship fleas but are stopped upon the enterance of the Balrog. Legolas fears for the group's lives, saying, "Ai! Ai! A Balrog has come!" Once more the group flees but when Gandalf is taken into darkness by the demon, Legolas becomes confused. He is immortal and knows little of death and the departure of the grey wizard hits him hard. However, after a short journey, they reach the woods of Lothlorien.
Here the Elf's spirits rise as he sings the song of Nimrodel to all the group and they meet up with Haldir. After much persuasion on Legolas' part, Haldir agrees to lead them into the forest but the Dwarf must be blindfolded. Gimli of course protests so Aragorn decides that everyone will be blindfolded. This hurts Legolas because he had never before set eyes upon the beauty of Lorien. However, they meet Galadriel and, after Legolas tells her of Gandalf's fall, they go to rest. The Elf however spends much time among the Galadhrim instead of his companions and learns much.
When they leave Lothlorien, not only is he presented with a cloak but also a new longbow and quiver of arrows.
The fellowship travels downstream and, after a couple days, arrives at Parth Galen. It is here that utter chaos ensues for the first time.