Make a second backup (with disk utility or carbon copy cloner) of your boot partition, then erase it. Do not skip this step! You need at least two copies of the data at all time, which means making a second backup before deleting the originals.
Install a blank copy of Leopard onto the empty partition, ignore any prompts to restore from a time machine backup.
On your time machine backup disk, open up the backups.backupdb file, open the directory named after your computer, then open the "latest" folder. All of your data is in there, you can copy apps and files and so on over.
Some apps, such as microsoft office, are better off installed from scratch instead of restoring a backup.
Some of your data is in "Library" directories. Copying this data over to the new system is a bit risky, I would only copy the stuff you know you need (for example, keychain and emails and textmate settings). Try to avoid restoring as much of this as possible ... nobody ever tests going downgrading software properly, you will run into issues if you restore it.
If something goes wrong with the system while messing around with your ~/Library folder, just delete it and log out/in again. A new one will be created for you with default settings, and you can start restoring from backups again - this time skip the one that caused problems.