how do I find out (for free) the cause of death for a person?

If it was newsworthy ("Local man dies in motorcycle accident") you can look up old newspapers in the library on microfilm. If not, you'd have to ask the family. It's on the death certificate but in most states you have to be a parent or child (or lawyer) to be able to buy a copy.

Call the family, tell them how saddened you were by the news, recall some anecdotes about the dearly departed, preferably ones that show him/her in a good light, and let them talk.

Ask their relations

As others have stated family or friends who know can tell you or has Ted has stated an obituary might have the information if it wasn't from natural causes.

Other than that there are privacy issues. Each state as its own laws about who, when and where a person can obtain a death certificate on another. I know for deaths in Texas it is 25 years if you are not a close relative such as parent or child or have a legal reason such as an attorney.

Tactfully ask the family; if you are a close friend they might tell you.

with researcgh