You can either install the itch launcher (it's their version of steam) and use it to download any games you buy through itch.
Otherwise after you download the game from the itch page, extract the folder, then run the .sh file.
If there isn't an sh file, the game won't have the penguin symbol, but you can get most of them to run if they're windows compatible, just right click on the game exe file and launch it with wine.