I know how to record with OBS, but when I try to record my League of Legends games, the video just turns black with only the mouse icon seen.
Recording or streaming League of Legends is somewhat tricky. The game uses 2 different windows: one for the client and one for the game.
The easiest way to stream/record League of Legends is by running the game in (borderless) windowed mode.
Now depending on whether you want to just record the game or the game and the client you might want to use the OBS Scene Switcher Plugin. This plugin allows you to automatically switch to the right scene when changing your focus. However If you're only interested in recording the game it's not necessary.
For the game recording itself you just have to add a scene with window capture. The window you have to select in order to stream or record the game is called League of Legends (TM) Client. If you have done this you should be able to record your games.
I would also recommend saving these settings in your scene collection since it's really annoying to configure these settings all over again if you have to restart the program.