With a single light source—let's assume it's a strobe—you can start with a diffused light (bounced off of a white ceiling or wall, or better still reflected in an umbrella or through a large silk or softbox) to lay the foundation for a high-key portrait. With a diffuse source, position your subject very close to the background—whether that's a light-colored studio wall, or perhaps a whitewashed wall found outdoors. The diffuse light source will minimize harsh shadows, and with the subject close to that background and the single source fairly far from the subject, the illumination from the key light will also serve to illuminate the background. This is especially important when working with a flash indoors, as the sun shining on a bright background outdoors won't require your subject to be close to the background.
If you'd care to make a high-key portrait outdoors with sunlight, you're likely going to be faced with two types of illumination: bright sunlight on a blue-sky day, or diffuse illumination from a lightly overcast sky. Both work just fine for high-key portraits, although the direct sun on a clear day is likely to create stronger shadows that could spoil the effect. Lightly overcast days, though, are perfect as they create the soft, wraparound light that eliminates deep shadows and makes people look great.
If you'd like to turn bright sunlight into a softer illumination for a high-key portrait, you've got a couple of great options. The first is to recruit a friend to assist you in positioning a large silk diffusion over the subject. This will essentially create a shadow in which your subject can stand, and it will soften the harsh sunlight and turn the diffusion silk into the new light source—one that's fairly broad and soft and quite attractive. But, you don't have to stop there. Remember that flash we were using indoors? You can implement it here as well, creating a strobe main light illumination to override the now softened sunlight. This can be helpful if you want to position a light just so, or if you need to restrict the brightness of the background. With strobe, you can expose for the bright background and bring up the strobe power as needed, whereas if you expose for the shadow created by the silk diffusion, a brightly illuminated background could risk being blown out.
Overexposing by a third- or a half-stop—or maybe even more—is the last step in creating a high-key portrait. In film days this process was trickier, but thanks to the histogram feature on your DSLR, you can check to verify you've maximized the bright tones toward the right side of the histogram without clipping them and losing detail—indicated by the histogram's peaks running off the chart to the right. Whether you're illuminating with strobe or sunlight, overexposure will help brighten the overall key and eliminate the details and textures you don't want without obliterating the ones you do. It's a fine line to walk, but the results are worth it. And, if you use your technological advantage, you can ensure you maximize the high-key look without eliminating important image-forming details.