AMD/ATI drivers for Radeon HD 6870 on Maverick Meertcat Live CD

That's a painful bloody title for a blog post I can tell you.
Download the installer from here to your Live USB key root directory. And make it executable:

chmod +x ati-driver-installer-10-11-x86.x86_64.run

Then reboot into the Live CD. Hit [CTRL+ALT+F1] and type the commands:

sudo /etc/init.d/gdm stop
cd /dev/shm
sudo /cdrom/ati-driver-installer-10-11-x86.x86_64.run

Answer yes to all the questions. Then run:

sudo cat > /etc/X11/xorg.conf << "EOF"
Section "Files"
 ModulePath   "/usr/lib/xorg/modules"
 ModulePath   "/usr/lib/X11/modules"
EndSection
Section "Device"
 Identifier  "ATI radeon 6870"
 Driver      "fglrx"
EndSection
EOF

To remove the "Unsupported Hardware" logo run this useful script from the Arch Wiki:

sudo cat > ./remove_logo.sh << "EOF"
DRIVER=/usr/lib/xorg/modules/drivers/fglrx_drv.so
for x in $(objdump -d $DRIVER|awk '/call/&&/EnableLogo/{print "\\x"$2"\\x"$3"\\x"$4"\\x"$5"\\x"$6}'); do
 sed -i "s/$x/\x90\x90\x90\x90\x90/g" $DRIVER
done
EOF
sudo chmod +x ./remove_logo.sh
sudo ./remove_logo.sh

and then just:

start x