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Kendra was introduced in What's My Line I, episode 2.09 of Buffy the Vampire Slayer. In this episode, Spike decides to contract the Order of Taraka, a ruthless guild of assassins, to take out the Slayer. When a mysterious young woman arrives in Sunnydale hidden in the cargo hold of an airplane, the obvious inference is that she's a member of the order, come to make an attempt on Buffy's life. That attempt comes just before the end of the episode, but Buffy is astonished when her attacker proudly identifies herself as Kendra the Vampire Slayer. And what's even more astonishing? She's telling the truth!
As Giles verifies, Kendra was Called after Buffy's brief-but-official death at The Master's hands in Prophecy Girl, the season one finale. The fact that there were two Slayers came as just a big a surprise to Kendra, who only attacked Buffy because she thought the blonde was a vampire. Which was a pretty big mistake, granted, but she did see Buffy making out with Angel (in full-on game face, no less). Kendra only appeared in two more episodes (three if you count Becoming II, in which she lay dead) but that was more than enough time for me to fall in love with this character.
For more about Kendra (and Bianca Lawson), check out the extras!