Plantar fascitis is a strain of the connective tissue that runs from the heel to the ball of the foot. If you are in intense pain, the first step you should take is aggressive rest: no athletic activity for a week or two, combined with wearing some sort of cushion in the shoe. This can be a soft foam insert with an arch support, available at a local drugstore. The idea is to cushion the area just forward of the back of the heel. You should wear an insert for several months whenever the body is upright, even for short trips to the bathroom at night.
So how can yoga be done without going barefoot? At first, just leave out standing poses and other asanas where weight is put on the feet. In the acute phase, care should be taken in all asanas that stretch the back of the legs. The muscles and fascia from the sitting bones down to the heels and along the sole of the foot are all connected, and stress will show up in the weakest link, such as in plantar fascitis. However, once free of pain for a while, these are the very asanas that will help you. Standing poses and seated forward bends will strengthen the legs, drawing weight upward instead of allowing it to collapse down, stretching out the backs of the legs. Perhaps the single most useful stretch is simply standing on a wedge or slant board, with the toes higher than the heels, and slowly lengthening the calves. (At the beginning this can be done with shoes on.)
Once you are ready to return to standing poses, it might be a good idea to cut up a sticky mat to fashion portable supports to place under the arches of the feet. Concentrate on the alignment of the feet and legs: Be especially careful not to roll weight onto your inner foot. Instead, distribute weight evenly across the soles of the feet.
Finally, be patient. Plantar fascitis can take up to three months to heal.