A dull sky can come from both capture settings and processing. In a scene dominated by blue, auto white balance may neutralize the blue and make the image look less vibrant. Try setting white balance to daylight, or better yet shoot RAW so you can correct white balance later.

A circular polarizing filter can also deepen a blue sky and improve contrast, especially depending on your angle to the sun.

For exposure, avoid using high ISO unless you need it for shutter speed. Lower ISO generally gives cleaner files and more flexibility. Be careful not to overexpose the sky, because blown highlights can’t be recovered.

In post-processing, small adjustments often help a lot: cool the white balance slightly, add a bit of contrast, clarity, vibrance, or saturation, and fine-tune exposure. Keep it subtle so the result still looks natural.

So the main steps are: use lower ISO when possible, consider daylight WB instead of auto, shoot RAW, avoid overexposing the sky, and use a polarizer when appropriate.