Club LOL is where K.K. Slider performs, and where Dr. Shrunk can teach you emotional reactions. This page explains how to unlock it, and what you can do there.
When you first start the game, Club LOL is not there. To unlock it, you have to first upgrade your Nooklings' store to the convenience store (see the shop unlock guide for details). Then you have to sit in your mayor chair in the town hall and make your town earn 100 points. (Just do the things around town that Isabelle asks, then go back to your mayor chair.) Finally, pay Isabelle to be able to build public works and change the town rules. The next time you play, Dr. Shrunk will be outside your house and will ask you to get the villagers to sign his petition. Talk to villagers and ask them to sign. Once you have enough signatures, go to the north part of town and talk to Dr. Shrunk there. The next day, Club LOL will open.
There are four gyroids on the stage in Club LOL. Before 8PM, you can walk onto the stage and check on the gyroids. If you have a gyroid in your inventory, you can swap it with a gyroid on the stage. This way, you can put a custom set of gyroids on the stage. The gyroids will 'perform' during DJ K.K.'s club nights, which are explained in the next section.
Starting at 8PM on every day except Saturday, DJ K.K. will do a DJ set at Club LOL. He will play his songs (see the list of K.K. Slider Songs), showing their album covers on the screen, and he will also include your town tune, and will sometimes take a break and activate the gyroids on the stage before he plays the next song. As explained above, you can put a custom set of gyroids on the stage whenever K.K. is not performing.
You can press buttons on the directional pad to dance while DJ K.K. is DJing. Press up to pump your fist in the air, press down to jump. Press left and right to do dance moves.
Starting at 8PM on Saturday nights, K.K. Slider will perform in Club LOL. You can talk to him and request that he perform a specific song (see the list of K.K. Slider Songs), or you can ask him to perform a song with a particular mood (such as an upbeat song, blue song, etc.) After he finishes the song, he will give you a copy of the song, which you can put into a music player in your house, such as a stereo or record player. He only gives one song per night, though, so once you get one song, he won't give you copies of any other songs you ask him to perform.
If you visit Club LOL before 8PM, Dr. Shrunk can teach you to express your emotions. Just give him some food (e.g. fruit). He will go on stage and do a stand-up comedy routine to teach you an emotional reaction. You can access these by tapping the purple tab at the bottom of the touch screen. The touch screen will show icons representing all of the emotional reactions that you have learned. You can tap and drag the icons around to put them in whatever order you want.
The final reaction that you learn is the Dr. Shrunk Dance. After you learn it, Dr. Shrunk will give you a yellow blazer that you can wear.
Here is a list of all of the emotional reactions that you can learn.