OK, the setting for the installed applications are stored in the folders in your home folder that start with a dot like .config or .mozilla, etc. So If you back up and move them to a new computer, the applications work just like before. This is for example what I did with my Firefox and XFCE desktop settings when I moved to a new laptop.
There are a few more things to consider:
1-You should back up the list of installed packages as well, as explained in the link in my comment above.
2-Some of your "system" settings are not restored in the home folder, for example the network (ethernet, wifi, etc) and their passwords are stored in /etc/NetworkManager/ so you may want to back them up as well.