How would I make my photos more 'vivid' but still natural?

The black edges on that photo are called vignetting. What kind of camera do you have? Do you have any processing software? If you do, bump up the saturation and clarity... Its really about your lens and camera set up to get sharp photos.

I cant say that I like this shot, but if this is what you are going for you need a good lens that offers a nice dept of field so that some parts like the grass is blurred. Then up the saturation a bit to exaggerate the colors. You could chip up the contrast a notch as well. The use a shaded boarder to finish it off.

Good Luck.

It's a variant of the cross-processing technique, there are tutorials everywhere online and most online photo editors now have a tool for that too

Up the warmth, the contrast down a tiny bit, saturation up a little bit as well.

But it's really the warmth that does it in my opinion. o:

Use Kodachrome.