Boot TinyCoreLinux from the CD you burnt. Choose the first option in the list to start the desktop.
At the bottom of the desktop you should see a number of icons - double-click on the icon that looks like a black square, this should open a terminal window.
In the terminal window type tc-install and hit enter.
Edit: alternatively, you can double-click on the icon shaped like the head of a screw, which starts tc-install directly.