I think what is happening is that you may have just stopped too soon and that your system was booting up as if the Option key were held right after the startup chime (bong, call it what you will) is heard- booting to a window that shows all the devices attached to the computer that are potentially bootable. If that is the case, then using the arrow keys to select the OSX Install Disk DVD and pressing "enter" (or clicking the right facing arrow if you are booting a PPC based Mac) will allow your system to startup from the installer disk to get you started.
In case I am reading your description wrong, insert the Leopard disk and restart your system. As soon as you hear the startup sound, press and hold the C key on your keyboard. Keep it held down until you can tell (or most likely hear) that your system is starting up from the DVD, then have patience while it boots all the way to the initial installer screen which can take several minutes.
Now-- you didn't ask but I will add that unless you don't have anything important on your disk that you really should not be doing an upgrade if you don't have a current backup. Although the vast majority of major upgrades between OS versions like your Tiger-->Leopard is go just fine, whenever you are dealing with LOTS of files being replaced/modified like this there is a too real possibility of something going whacko in the process. Just wanted you to keep it in mind! 😉