If no way to have an internal hard drive installed into your iMac, then you will need to purchase two good quality, large capacity FireWire 800 (fast data transfer connection) external hard drives.
FIreWire 800 drives will give you an operational speed close to the same speed as your iMac's internal hard drive.
One external hard drive will be used as your iMac's main working drive. The other drive is to be used to create either cloned, bootable backup drive or to be used with OS X Time Machine backup app.
To install OS X Snow Leopard onto an external hard drive, if your iMac's optical drive is still working, power up your iMac holding down the C key on the keyboard and immediately insert the install disc into the optical drive slot on the side of your iMac.
Your iMac should boot up to the system that is on the install disc.
Once you are in the Installer app, go up to the main menu bar and quit the installer.
Then on the main menu bar launch the Disk Utility app and format the external drive for Mac OS X Extended ( journaled ) format with a GUID partition scheme.
You can decide if you want one larger partition on break the drive down into more than one partition for data storage purposes or not.
Once the drive is formatted, quit Disk Utility, relaunch the OS X installer app and proceed, following the instructions to install OS X Snow Leopard onto your external drive.
Once installed, you'll be prompted to restart your iMac and it should automatically find where OS X is installed and boot up your Mac to OS X.
From there, you can go into OS X Preferences Panel and select the software update feature of OS X to update your OS X version to OS X 10.6.8 and all of your Apple installed apps.
In OS X System Prefrences panel under Startup disc icon, click the icon and set the startup disc for the external hard drive that shows your currently installed OS X system.
This OS X will know where OS X is always launched from and won't have to hunt for it when you always startup your Mac.
You will have to reinstall all your third party applications, too.
Good Luck!