The Fire Walking Festival (火渡りまつり, hiwatari matsuri) is held near Takaosanguchi Station on the second Sunday of March each year, and attracts about 3,000-4,000 visitors. The main attraction is the monks walking barefoot across the embers of burning wood to cleanse themselves of evil spirits, pray for world peace, longevity, safe passage in life, and general health and safety.
The event starts at 1pm with a procession of chanting monks walking into the main event arena (held in a car park just off the main road). This is followed by rituals and performances by the monks such as fending off evil spirits with various weaponry, flaying their bodies with branches dipped in boiling water, and the reading of a long-list of names of those who have paid for the privilege.
Following the pre-ceremony a square stack of fern leaves and wood is set alight. The heat from this bonfire is intense for about 1-2 minutes until the fern branches burn and the monks begin dowsing the flames with buckets of water. They then spread the ambers and prepare two strips through which they walk barefoot and chanting. Members of the public can also pay a small fee to walk across after the monks (by this stage the ambers are no longer smoldering and there should be no worry of burning your feet).
Note that although the event begins at 1pm, if you want a good view you should aim to get there about one hour beforehand. There are several stalls selling the usual festival fare (takoyaki, fried chicken, chocolate bananas, etc.). The pre-ceremony and burning of the bonfire takes about 90 minutes and the event officially ends at 3:30pm.
Note that the Fire Walking Festival does not take place at Takaosan Yakuouin Shrine itself, but in a car park a short walk from Takaosanguchi Station. Access is via the Keio Line from Shinjuku Station. It takes approximately one hour and costs ¥390.