How do you pronounce the word Shaman?

As an American I consistently say /ˈʃæmən/ and don't recall ever hearing anyone, American or otherwise, saying /ˈʃeɪmən/.

The latter might be a regional difference? I've lived in a half dozen or so different places and haven't come across it. Still, I haven't covered them all.

Per Peter Shor's comment /ˈʃeɪmən/ is the primary pronunciation in at least one dictionary of British English.

Note: Since I relied on personal experience as a native speaker for this answer I'll mention that my formative speaking years were spent in the Northeastern United States and that I have spent significant time living in the South Atlantic, Midwest, and Mountain regions of my country. I consume media mostly in American and British English.

I hear both "SHAME-an" and "SHAW-man" here in the U.S. I just listened to a 2009 lecture on shamanism by a U.S. expert on the subject, Dr. Stanley Krippner (in order to copy-edit a transcript) and in that lecture, a keynote talk for the International Association for the Study of Dreams, he consistently says "shaman" like "SHAME-an," and "shamanism" like "SHAW-man-ism." But I'm trying to find a link to a Krippner talk that's available to the general public, and so far I'm only finding him saying "SHAW-man" -- so Google him yourself, and see what you can find!