TAS Season 1, Episode 2: Yesteryear

This episode was clearly a large influence for the writers of the first Abrams movie, and rightly so. They do a good job of explaining Vulcans in this episode, and they do a decent job at giving us some insight into Spock’s character.

Plot

Captain Kirk and Spock return from a time-traveling research project they have been conducting with the use of the Guardian of Forever and Starfleet historians. When they emerge from the portal, no one on board the Federation starship Enterprise recognizes Spock. The ship's first officer is instead an Andorian, Commander Thelin.
In the new timeline, history has recorded that Spock died at age seven undergoing the Kahs-wan ordeal on Vulcan. However, Spock remembers that when he took the Kahs-wan, his life was saved by Selek - an adult relative - when a desert creature with poisonous claws called a le-matya attacked them. Kirk hypothesizes that Selek was actually a time-traveling Spock. While Kirk and Spock were in the portal, the Guardian and historians had run a scan of recent Vulcan history. The pair realize that as they were observing the birth of Orion at the time, Spock could not have been in two places at once to save himself as a child. Spock must go back through the time gate, and save the life of the child he was. Thelin is supportive of Spock's efforts despite their consequences on his own existence.
Spock assumes the identity of Selek, a distant cousin of Sarek, and is welcomed into the home of Sarek and Amanda Grayson.[note 2] "Selek" journeys into the desert to find his younger self, and saves the boy. However, I Chaya - Spock's pet sehlat - is gravely wounded. The younger Spock runs to fetch a Healer. The Healer tends to I Chaya and informs Selek and Spock that it is too late for an antidote; he can only prolong I Chaya's life, during which he will be in pain from the poison, or euthanize him. Young Spock chooses the latter. By making this choice, Spock has thus chosen the Vulcan way of life - logic and emotional control - and his elder self, successful in repairing history, returns to the restored present day, but not before teaching his younger self how to perform the Vulcan nerve pinch in order to deal with some school bullies.