How do you take black and white photos with a fujifilm finepix a500?

Answer 1

Indeed you can't, there's no “black and white” option in the A500.

If you want to create black & white photos, your only option is to use an image editor that offers that function; most do, including some free ones such as Google Picasa, FastStone Viewer or The Gimp (and of course commercial ones, such as Photoshop, PhotoPaint, Paint Shop Pro, Photoshop Elements, Microsoft Image Suite, etc, etc.).

http://picasa.google.com/features/index.html
http://www.faststone.org/FSViewerDetail.htm
http://www.gimp.org/

Actually, taking the picture in colour and then converting it to black & white in post-processing is ALWAYS the best option, even with cameras that do offer that function with a wide array of variations (color filters, etc.); that way, not only you keep the original colour version in case you end up liking it more than the B&W one, but most programs offer a much greater control over the B&W conversion process, letting you decide in terms of colour filter, tonality, etc.

Answer 2

From a quick review it doesn't appear that you can. Check your Owner's Manual.