Here’s how I capture hummingbirds sipping nectar with mountains and sky in the background making bands of blurred color:

Put the pot of flowers on the deck rail where there is a distant view of mountains. (This will work with other distant views or objects as well. Try to find a pleasing background  with nothing between the flowers and the background.)

Use a telephoto and experiment with aperture settings until your flowers are sharp and background blurred.

A tripod helps to support a heavy lens while waiting to photograph.

To capture the hovering wings, use a fast shutter speed.

Optional: Add a little fill flash to lighten shadows or light up the iridescent feathers of the bird.