If you don't have a funeral of any sort, Zany Mouse, then you arrange to have the body either:

1. cremated...or...
2. buried in a local cemetary

Those arrangements are naturally made through a funeral home, but they do not require a public gathering with a service of some kind, which is what a funeral is.

You can also have what is termed a "reception" which is a public gathering at the funeral home at a certain time, but it's not a funeral service, as such.

You are required to do various legal paperwork, and the funeral home will assist with that, as well as with placing a death notice in the newspaper if you wish. They will provide copies of the Death Certificate which will need to be sent to various banks, credit card companies, and so on...whoever needs to be informed.