What settings should I change on my camera to achieve what I want?

http://yourshot.nationalgeographic.com/photos/4348979/

For example, I would like the sunflowers to pop a bit more and be brighter, but not lose any of the sky. What settings would I need to adjust on my camera?

Added (1)..

Added (2)..

First you need a wide angle zoom lens like a Nikkor 10-24 mm or Canon 10-18 mm (depending upon which brand digital SLR you have.

Other than that, the photo could be a straight shot out of the camera.

You can use a program like Lightroom 5 to enhance the images you capture if necessary.

Many novice photographers like to set their cameras to "vivid" to add punch to their images

If you shoot in RAW, you can make modifications that are reversible if you happen to go too far with your clarity, vibrance, saturation and make minor adjustments in the highlights and shadows using Lightroom 5. The Graduated Filter can be used to darken the sky, leaving the foreground alone

To get a rich colour in the sky AND have the sunflowers 'pop' then you have 2 choices;
- use a grad and filter to 'hold back' the sky exposure by a couple of stops & expose for the sunflowers
- take 2 exposures, one for the sky (underexpose it a bit for richness) and one for the sunflowers & blend together in post.

Using fill flash (& exposing for the sky)would work, but only for the front row or so of sunflowers.

The scene has too high a contrast range to correctly expose for in a single frame - which is why the sky looks a bit washed out and the sunflowers don't really pop in the image you linked to.

I think the shot is good as it is, but understand what you mean about bringing the flowers forward.
You could over expose by half a stop but that would ruin the sky.
Or, if you have a strong flash, try lighting up the nearest sunflowers with it.

The settings used for that shot are sitting right there by the picture.