Debian Linux 8 (Jessie) came available this autumn. It still runs on an old PC, in my case Asus EeePC laptop, with only 4 GB SSD hard disk.
In order to install Debian you need to download the ISO-file and burn it on a USB-stick. I chose Debian Netinstall which is available here: http://cdimage.debian.org/debian-cd/current/i386/iso-cd/ . There are number of burning sofware out there. Use Win32DiskImager, UNetbootin on Windows or command dd on Linux to prepare your bootable Debian USB-stick.
Make sure you tap down Esc while powering your EeePC in order to boot from USB. Then, off you go and install Debian. There is nothing much to tell about this phase. If you are setting up Linux for the first time pay attention to every screen you see.
Since there is not that much space available, only 4 GB hard disk, you have to compromise. I decided to wipe out GIMP and LibreOffice. They both are too heavy for my old EeePC. This is how you do it what comes to LibreOffice:
sudo apt-get remove --purge libreoffice*
sudo apt-get clean
sudo apt-get autoremove
After the uninstall of GIMP and LibreOffice there is more than 1 GB free space available for the forthcoming updates. I'm very satisfied with this result. My EeePC is still going strong!
EeePC 4G meets Debian 8 (Jessie)