Having a faded look in a photograph is not an effect that everyone will find to their taste. Nevertheless, with the right photo and the correct output media (typically Instagram), said effect can be rather compelling.
A 'fade', as it is often called, is realised by lightening the 'blacks' in an image (the very darkest tones) such that they take on a dark-grey shade instead of, well, black. Lightroom’s Tone Curve is the perfect tool for this selective black-brightening requiring only three steps to affect the change:
Ensure that your Tone Curve panel is operating in Point Curve mode by depressing the Point Curve icon.
Place a few supporting points on the curve so that subsequent adjustments don’t send the whole graph into a wildly hallucinogenic tailspin.
Lift the lower left adjustment point to dial in the desired amount of fade.