When does Beast Boy show up on Teen Titans? I know he got his powers when he was eleven, but I don't know when he shows up on Teen Titans for training, team work lessons, and being a hero.
It's not clear if you're asking about the TV show or the previous comic book continuity. I'll try to answer both ways, just to be safe.
In the TV animated series that began in the early 2000s, Beast Boy was one of the five founding members of the team. (Along with Cyborg, Robin, Starfire, and Raven.) By sheer coincidence, they all bumped into each other one night, as seen in the episode "Go!", and ended up deciding to work together as a regular thing. So in that fictional universe, he could honestly say: "I've been a member in good standing of the Teen Titans for as long as there's been a Teen Titans!"
In the original comic book continuity, the Teen Titans team concept began in 1964 -- with Robin (Dick Grayson), Kid Flash (Wally West), Aqualad (Garth of Atlantis), and Wonder Girl (Donna Troy) as the four founding members, and Speedy (Ray Harper, Green Arrow's sidekick) joining up very soon after the team was formed.
Beast Boy (Garfield Logan) existed separately from the Teen Titans in the DCU for a long time before finally becoming an official member of "The New Teen Titans" when the team concept was relaunched in a new monthly series, with seven core members, in 1980. Garfield Logan was one of four new recruits to the team at that time — the three "old-timers", who had all been friends and teammates off and on for years before that, were Robin, Wonder Girl, and Kid Flash; and the other three members were three newly-created characters: Starfire, Raven, and Cyborg.
In New Teen Titans #1 in 1980, when he joined the team as it was being reorganized, he also announced that he had recently decided to change his superhero alias to "Changeling." (He stuck to that until sometime in the 2000s, I believe — then, probably due to the real-world success of the TV show which told millions of people that the green boy's name was "Beast Boy," DC had him switch back to using the alias "Beast Boy" in the regular comic book continuity.)
Note: In both the comic book continuity of the DCU, and the separate continuity of the "Teen Titans" animated series, Beast Boy had worked with the separate superhero team known as "the Doom Patrol" for a while before he ever met the other teenage heroes who became "Teen Titans." So, despite his probably being the youngest member of the team when he joined (in both versions), he already had a fair amount of training and experience in using his shapeshifting powers to do heroic deeds. The other Titans didn't need to "start training him from scratch."