Many ways to do this. Most involve selecting the part of the image you don't want and substituting something else.
Check out this tutorial to give you some ideas. http://tv.adobe.com/watch/the-russell-brown-show/masking-basics-in-pho toshop-cs5/
Hope this helps.
If you meant exactly what you said, that is, that you wanted only a completely neutral background, then here is an example using your original background, which is now neutral. If you meant something else, then more details would be needed. If what you really need is to eliminate all of the textured background then that is a bit more work.
Sorry, I've been too vague in my question.
I did take the pictures of this juvelery pretty fast - and thereby made some mistakes. One mistake was to use a cloth (though black) as background - but in harsh sunlight. This makes the texture of the cloth stand out. What I want is to swap this cloth background with a color or gradiant.
I'm a bit shamed to show my first attempt
First attempt was to place an solid color layer below the image, create a mask and just paint away the cloth.
The magic wand is not good to select on the cloth. Quick selection seems a bit more usefull on this cloth.
Is this layer mask, paint away the right approach?
What's the most efficient way to select the cloth - having these not that regular edges of the links of this chain?
I thought you might be asking to remove the textured background. The simplest approach, though not always possible, is to reshoot the jewelry. If you must work with the image then painting in a mask is one approach which may work for this image, but I would suggest eliminating only the textured areas that have no shadows. In other words, keep the shadows. If you are not familiar with other selection techniques then painting a mask may turn out to be the quickest solution for you.
Personally, I would use the pen tool to create paths, which you can then turn into selections and refine them if needed. The nice geometry of the rings should make this work well. Alternatively, you could try using the magnetic lasso tool as the black edges of the shadows should trace nicely.
Some food for thought, in no particular order:
Some visuals to get your creative thoughts flowing...