The oil baths Nancy spoke about were a practice taught to her in Mysore alongside the (asana) practice, as an Ayurvedic treatment to counter the amount of (Ayurvedic) heat in the body generated from the practice. If the heat stays in the body, it can tire you and lead to other symptoms like drying your skin out. Maybe it helps with inflammation but I’m only guessing.

Once a week, on your rest day from your Ashtanga yoga practice you should have an oil bath, this is done by using an oil with properties that remove the heat. In hot climates she was recommended to use coconut oil, and cold climates sesame oil (basically if the climate is cold enough that the coconut oil turns hard you should use sesame oil).

You should rub the oil on all of your skin head to toe, including your scalp, leave it on for 10 mins and then have a shower to wash it off, and then apply again a second time. The second time you leave it on for 30 mins (and then wash off). On the first application the oil kind of sits on the skin but on the second time it sinks in.

3 weeks a month you should use the appropriate oil from above, and once a month you should use castor oil. Castor oil is very heavy/thick and hard to get off (especially from your hair) so you can use soap nut powder if you can find it (they have it in India at least), or apparently ground mung beans (you can do it in a coffee grinder) also do the trick. Hot water to rinse also helps. Also you might want to choose to do it somewhere you can easily clean!!