There are several facts that need confirmation or need to be discovered. I can't seem to find GreeK's notes on this one. :(
For example, I'm not sure if you apply the body to the coffin, or the coffin to the body (by clicking the four-pointed star). The one I did was long enough ago, I can't fully remember. I seem to remember that I built a coffin in a building, then took it out and fiddled around with the "use on" buttons so I wouldn't accidentally bury the body without the coffin.
Also, once a body is in a coffin, I think it can not longer be moved. However, this is also another thing that needs confirming.
I am pretty certain you can bury a person with their clothes still on, but not notes or other objects that they held. Only bodies can be put in coffins.
Funeral pyres are pretty much the same way, though I've never used one myself. If anyone has done this, I'd appreciate the info! Thanks!