K.K. Slider will visit your island once you have a 3-star rating, and will visit again every Saturday.
Unlocking K.K. Slider Concerts
Before K.K. Slider will visit your island, you have to move in 10 residents, then talk to Isabelle in the Resident Services Building and ask her about Island Evals. You need your island to have a 3-Star rating before K.K. Slider will visit, so follow Isabelle's advice, and check with her about your current island eval.
First K.K. Slider Concert
The day after Isabelle tells you that you have a 3-Star rating, K.K. Slider will hold a concert at the plaza in front of the Resident Services Building, where he will play the song Welcome Horizons.
Saturday K.K. Slider Concerts
After K.K.'s first concert on your island, he will visit every Saturday, and you can request a song starting at 6PM. (See the list of K.K. Slider songs for a list of songs you can request.)
After his performance, the song will be in your inventory, unless you requested a song that he doesn't know.
If there is a special event on the plaza on a Saturday, K.K. Slider will visit on Sunday instead.
K.K. Slider will make a special appearance in your town plaza on your birthday, and will play K.K. Birthday for you.