Here is the why and how I recommend you photograph the sky.
It's important to have your own personal library in which you can use to replace the sky in your future photos (or older ones), because let's face it, sometimes, you go photograph a landscape, landmark, cityscape, people, or even products, and the sky is overcast or without any clouds or drama.
There is nothing wrong with a blue sky without clouds or a sunset or sunrise without any, but sometimes, having some clouds can increase the quality of the photo. However, the weather does not cooperate all the time to give you the perfect sky with beautiful clouds.
Below is a photo that I took when I was living in Japan of the Osaka's Temple with the sky without any clouds and one with added clouds, just to illustrate.
If you are against sky replacement or you are a purist type of person, there is nothing wrong with that, but you are limiting yourself and your photos in my opinion. When you see a beautiful sky with interesting clouds, why not take a few minutes to photograph it? It won't take that much time or storage space either. But of course, if you are photographing the sky to use later, you need to have some things in mind.
Don't point your camera up to photograph the sky, because it won't match properly later when replacing it (it's not impossible to make it this way, but it will give you more work, especially if the angle is way too different); instead, try focusing on the horizon, leaving a bit of the horizon on the bottom part of the photo. Make some photos with the sun in the frame, outside the frame, in the middle, on the right, on the left, and so on, and with that, you'll have a lot of options later to choose from.
And of course, sometimes, the sky is way too gorgeous, and just a photo of it can make a beautiful photo or print!