Windows version (Click download on the topmost one)
Open the .exe file you downloaded previously, if Windows Smartscreen stops you from running it, click "Know more" and "Run anyways".
If Olympus asks you if you want to update, click "Yes", and wait until it updates, then click "Restart Olympus."
You should see a tab at the left tagged "Installations". Click on "Manage" or "Add installation"
If you have the game on Steam it should detect the Installation Folder automatically, but if you have the Itch.io version you should manually select Celeste.exe. Be careful to not have special characters on your file path.
For me, my path was D:\SteamLibrary\steamapps\common\Celeste
Once selected, you should install the latest stable version.