The subject says it. I would like to be walked thorugh the procedure
(photoshop ) for creating a a gradient (probably grayscale) which
starts from 80% black and VERY gently ends in 0% black without a
noticeable end point (has to merge with the background white) Also,
everytime I try I also end up getting banding in the gradient at
various points.
I have heard of adding 'noise' but when I try to do this in the grad
editor the whole thing becomes transformed into a colored gradient
rather than black and white.
Also have tried curves to control the sudden visible ending but the
end shows in any case.

I don't know what version of Photoshop you're using, but in later
versions, the "Add Noise" filter includes a selection for
"monochromatic."

You may find this helpful:

http://www.imouthere.com/pdf/Photoshop_Gradient_Blending.pdf

thanks for the help on banding, pinkfreund. I was using (or trying to)
the Noise setting inside the gradient editor. Not the noise menu
inside the Filters menu. Thanks for pointing me in the right
direction.
However, the gradient still doesn't blend seamlessly into the white
background. Have also tried (additionally) using the blur tool at the
edge. Still doesn't do it
I am using photoshop 6
(is there any inexpensive software which could do this easily and
WELL? say, a plugin or something?)

I like Harmware sTile (seemless Tile)-FREE. IMHO, it has the best
gradients I've ever seen. http://harmware.com/downloads.htm

I'm going to assume that 80% gray is RGB 51 51 51 (20% of black).

So, load and install sTile. Choose New to choose a size. Select
"Gradient" Two-color to make a gradient. From Color: 51 51 51. To
Color: 255 255 255.

Select the direction you'd like the gradient. (hint: you might want to
reverse From and To if you choose Eliptic fade. You might choose that
to make sure the fade is symetric about whatever you're looking for.

Also, check out the Multi-Gradient design as well. You could fade from
80% to 20% at one rate and fade 20% to 0 over a longer range. Your
results may vary.

Have some fun and apply the Gausian blur as well.

What color depth are you using for
   a) the image file?
   b) your video card?

For (a), make sure you're set to RGB color and 8 or 24 bit color under
the Image: Mode menu

For (b), banding often occurs when your video card color depth is set
to 16 bit or lower.  I would change to 24 or 32 bit color.

You shouldn't be getting any banding or an abrupt end to the gradient
if both of these are set appropriately.

--Joey