I use Jasc Paint Shop as may image editor and despite having read the help file on the subject I cannot manage to change a specific colour in an image to transparent. For example, I would like to to change the white colour of my avatar to transparent.

Maybe this <https://superuser.com/questions/354895/is-there-a-way-to-convert-white-to-transparent-in-paint-shop-pro-9> may help.  Not sure which version of PSP you are using but you might find a similar procedure for earlier versions.

Thank you. I shall check it out.

Just learned:

in the freeware that I use (PaintNET) I can use the "Magic Wand" in global mode (SHIFT pressed). Mark a pixel with the color to change.

Then "Delete" and done.

 

BUT: be aware that for real life pictures/photos you have to use the tolerance slider to get satisfactory results. Might need a few try and undo cycles.

 

 

That would be the result in PaintNET workspace (the grid pattern stands for transparent and interferes with the lines).

But I am not sure how (which format) would allow you a transparent avatar on a website.