For starters, don’t position your subject where they’re staring into the sun. Turn them away, so the sun is at their back. Not only will this help your subject stop squinting, but they’ll appear more flattering as well. You’ll now be shooting a shadowed subject with a bright background. To get the correct exposure for their face you’ll want to use the spot-metering mode in order to measure the illumination only on the shadowed face while avoiding the bright background. Open up a bit more (with a smaller ƒ-number or a slower shutter speed or higher ISO) than might otherwise be indicated by the meter reading in order to make a slightly more flattering high-key portrait.
Without any light modifications, this scenario will work better than a subject facing the sun, but it’s not the most refined lighting you’ll ever see. To improve it, you’ll want to modify the light. You can do this with a reflector—bouncing illumination from a white card or silver flex fill to illuminate the shadow side of the subject. Be careful to position this reflector so that it’s illuminating the subject from a pleasing angle. Otherwise, if you’re just bouncing light from any old position, it won’t look flattering—for instance, if you reflect the light from below you’ll create monster lighting. Adding more light to the shadow side of the subject will also result in a background that’s less blown out. It will still be bright, since it’s overexposed compared to the shadowed subject’s face, but not as dramatic as it would be if you didn’t use any fill in the first place.
In lieu of a reflector, you could also consider using a light source—like a hot-shoe-mounted flash—to illuminate your subject’s shadowed face. The real benefit here is that you can really increase the power of this light source in order to more evenly balance the subject illumination with the background—or, in fact, to overpower the ambient background light and make it go darker relative to the subject’s illumination. This technique, generally referred to as “overpowering the sun,” can be done with speedlight-style flashes or, better still, a more powerful battery-operated studio-ready strobe system. With such an off-camera strobe, you also have the added benefit of a more finely controlled lighting pattern—the ability to position the light and modify it (say, with an umbrella or a softbox, for instance) for the best effect on the subject, as opposed to simply dumping a bucket of light on the subject from the camera position. That may be effective for basic illumination, but it’s not especially nuanced. Using an off-camera strobe, and perhaps a modifier like an umbrella, gives you studio-caliber lighting control even in bright sunlight.
If you don’t want to carry lights and lots of modifiers, another approach is to scrim the sun. With a broad sheet of diffusion (called a silk or a scrim), you can eliminate the harshness of the direct sunlight and instead turn it into beautifully diffused light. This also affords you the opportunity to move around and work the light in a way that straight sunlight, or even a battery-operated strobe system, doesn’t quite deliver. There’s almost nothing more attractive than bright sun through a diffusion scrim, a practically perfect source for portraits. Yes, you can use it as a key light with the subject facing in the direction of the sun, but you can also return to the original, appealing pose with the subject facing away from the sun and instead use the scrim to diffuse the light falling onto the subject from behind. It will help keep the hair light from appearing to harsh, in particular, though it will also help to generally soften the light that’s striking the subject. Best still, with this approach (and enough helping hands), you can combine this technique with the reflector for frontal fill and create a nice, nuanced three-point lighting approach without spending one electron on generating the light.
But what if you don’t want to carry all that stuff and you just want to use the natural light at your disposal? Then, instead of simply working with whatever light you’ve got, you’ll want to move around and position yourself and your subject deliberately in relation to the light. Long story short, you’ll want to get out of direct sun and into a position where the light that’s illuminating the subject is reflected—either from a nearby building or trees, or from open sky, or even reflected from the ground. This kind of position is typically described as open shade—out of direct sunlight, but still brightly illuminated due to the indirect illumination. Open shade can easily be found just inside openings—just inside doorways, for instance, where the structure provides a natural opening to direct the illumination. Or under tall trees, where the shade isn’t oppressive and dark, but instead serves to simply diffuse the direct sunlight. You can even find open shade simply by positioning your subject in the shade next to a building.
Once you learn to move around to where the light is ideal, you won’t hesitate to head outside even during midday when your portrait subject wants an outside shot.