You can usually install anything into your "home" directory, it's just a bit tricky.
I have added this to my file /etc/profile
if [ -d $HOME/.local/bin ] ; then
if [ -d $HOME/.local/lib ] ; then
(Be careful with the .local/lib directory, as viruses might be implemented in libs you install.)
Now, when you compile stuff from source, you should pass the parameter --prefix=$HOME/.local to the command ./configure.
When you have binary files you want to execute (which don't depend on installed data), put them in your ~/.local/bin directory. Then you can execute them from the terminal/console/shell/... or your desktop (tested on Gnome).
Any further questions?