A program I have used is
Pinta, which is a GTK implementation of Paint.net version 3; it may thus look familiar to people who have used that other program. It has good support for image layers, although obviously nothing like as much as the
GIMP. Make sure that you have the layer toolbox opened and visible on screen (see the right hand side of the screenshot); this can be enabled from
View > Tool Windows > Layers. At the top of the menu bar is the layers tab, which has options for adding new layers, merging layers, altering the various transparency levels and more.
It is possible to do much in
Pinta with layers as this tutorial demonstrates, and this is an excellent introduction to the programs's layer functionality. It is apparent that backgrounds and objects can be removed, changed, or made transparent. Other photos or objects can be superimposed upon existing pictures and then the result merged and saved as a new file. The
GIMP has more options and functionality, but Pinta will probably suffice for relatively straightforward image editing with layers.
As a note, the version of
Pinta in the repositories is version 1.1; the latest available version is 1.3, which has some improvements in layer handling and one or two bug fixes. In particular, layers can now be rotated and zoomed, which may be useful in some projects. The latest version is available as a
sudo add-apt-repository ppa:pinta-maintainers/pinta-stable
sudo apt-get update
sudo apt-get install pinta
Instead of the
PPA, you can of course build the very latest version from source using the stable source code or the GIT development code; see here for more instructions.
Note: I have just successfully compiled the Git version, and the version from there is labelled as 1.4, and there are a few other minor bugfixes and changes. However considering this bugreport regarding saving images, which may affect some users of the Git development version, it is probably best to use the stable PPA version.