In fact, the answer to this question is simple: nothing. Although the best thing you can do is probably leave - and let the villagers and monks deal with their loss and rituals. It is no place for tourists.
Let me tell you why.
Of all places in the world you can end up after 7 days of trekking, I ended up in Korzok - a village of around 1300 people on the northwestern bank of lake Tso Moriri. At an altitude of 4,570 meters, it is among the highest towns in the world and consists for a large part of (semi-) nomadic families.
After 7 nights of sleeping in a small tent, using wet-wipes as shower material and no laundry, Korzok sounded like heaven when I arrived. A great place to rest, stock up on supplies and just hang around for a few days until I found horsemen to join to Kibber in Spiti Valley.
Little did I know that the Head Lama of Korzok Monastery, Langna Rinpoche, had died in a car accident on the Leh-Manali road just 2 weeks before. The 300 years old monastery, belonging to the Drukpa Lineage, and home to about 70 monks, had transformed into an active rite centre where the entire town came together and participated.
Tibetans believe that after death the consciousness takes at least 49 days to travel from one life to the next.
Prayers conducted by the monks and villagers assist the dead through this journey and help to guide them towards a good rebirth (reincarnation). For this reason, the dead body of the head lama was placed inside the gompa and surrounded by the monasteries 70 monks who were performing all sorts of rites: chanting prayers, blowing horns and beating the drums.
This was all broadcasted by large speakers and audible from every corner of the town. The villagers did their part by coming to the monastery several times per day and join in prayer or receiving blessings from the remaining lamas - during which time they temporarily closed down their shops, restaurants or guesthouses.
Finding food became a proper mission during the daytime.
I was staying with a local family in Korzok who provided me with breakfast, dinner, and a room with floor mattresses. They invited me to come to the gompa everytime they went. I did join them a few times, but each time felt a little like an awkward outsider - even though the people tried their best to make me feel welcome. It was like an intimate affair between the monks of the monastery and the villagers who all lost the head of the family.
So when I finally found two donkey men to take me across the mountains to Spiti Valley, I was relieved. I could leave Korzok and its people alone for the remaining of those 49 days. According to Tibetan believes, by then, the people have had time to grieve. And through their active participation in the rites, they can rest assured that they have done everything they can for the departed.