What would Buddha advise to farewell when one of your parents died? Perhaps some Buddhists will say death doesn't really exist, but in any case, when your parents die, there is something changed.

What would Buddha teach to say goodbye to your parents. Probably all kinds of feelings may be there and that is good, but worry a lot wouldn't be very advisable. But is it 'advisable' to feel joy or sadness. 

For short, how to say goodbye when someone close to you died?
You can do transfer of merit. 

More on this see:


How can merit be transferred?
Transfering merits
Sharing merit in Theravada Buddhism
Actions taken to transfer merit
Does Theravada believe in feeding food to hungry ghosts?


Also you can do a:


offering of cloths to the monks in memory of the dead (monks cloths were initially made of the cloth used to wrap the dead bodies)
organise a dhamma talk for the benefit of the dead (generally the night before the almsgiving mentioned below)
organise an almsgiving for the benefit of the dead (generally at 7 days, 3 months, then annually)


Some of these are covered in: Buddhist Ceremonies and Rituals of Sri Lanka by A.G.S. Kariyawasam