Kendra's training was more traditional than Buffy's- she was given a Slayer handbook.
Kendra become active as a Slayer after Buffy died fighting the Master. When Spike found the Du Lac manuscript and the key to deciphering it, signaling that he would be trying to revive Drusilla, Sam Zabuto sent Kendra to Sunnydale.
She appears to have all the same abilities as Buffy - and similar fighting style - also she has not mastered the ability to sense vampires, since she mistook Buffy for a vampire based on her kissing Angel. She is not like Buffy another way and that is she doesn't have friends and family around her to support her for her normal life and Slayer life.
After helping Buffy stop Spike and Drusilla, Kendra returned home, coming back to Sunnydale, when Angelus stole the sarcophagus of Acathla, to provide Buffy with a sword that would aid in defeating the demon. She was killed by insane vampire, Drusilla, while trying to protect the Scoobies.
Buffy: I don't take orders. I do things my way.
Kendra: No wonder you died.
Giles: Not to my knowledge. The new Slayer is only called after the previous Slayer has died. ....Good lord, you were dead, Buffy.
Buffy: I was only gone for a minute.
Giles: Clearly it doesn't matter how long you were gone. You were physically dead, thus causing the activation of the next Slayer.
Kendra: She...died?
Buffy: Just a little.
Giles: Yes.
Kendra: Right. Of course. And I imagine she's a cheerleader as well.
Giles: Actually, she had to give up cheerleading. It's quite an amusing story, really.....
Buffy: You named your stake.
Kendra (embarrassed): Yes.
Buffy: Remind me to get you a stuffed animal.
Buffy: Nope. Must be in the handbook. Right after the chapter on personallity removal.
