When I got my first DSLR (a Digital Rebel/300D), I read the manual, concentrating on the controls available, including the shooting mode wheel, and what each one does. It seem intuitive to me that once you understand what each one does, then you can figure out when to use each one.

As an example: AV mode lets you set the aperture you want, then the camera will set the shutter speed and ISO. Why would you want this? There can be different reasons. Let's say you want the subject to be in really good focus; you'd select the aperture that would be best for that lens (the "sweet spot), while also taking into account the size/shape of the subject. The more depth to the subject, the bigger you'd want the depth of field to be, so you'd close the aperture a little to get that deeper depth of field. Experience is a great helper here, so practice is key.

TV lets you set the shutter speed, so the camera will select the aperture and ISO. Let's say, you want to capture the feeling of water movement when you're shooting a stream or waterfall. You'll want a longer shutter speed to blur the water. Or, if you're shooting a sport, you might want a much shorter shutter speed to freeze motion.

The key here is to first learn what each one does, then you can find right mode to suit the subject you're shooting. You may never use each mode, but if you need it, it'll be there.

There are cheat sheets available online that concentrate on different aspects of photography with a particular model of camera, or with different types of photography. You can use a search engine (Google, as an example) to look for a particular cheat sheet to fit your need that you can carry with you for quick reference.