It's simple enough.
1. Download Lion from the Mac App Store.
2. Once it's downloaded, open Disk Utility.
3. In Disk Utility, select your hard drive (not the hard drive partition, the HDD itself) and click the Partition tab.
4. Below the partitions, click the "+" button, select the new partition that appears, and enter 8.0 GB in the size box. Click Apply.
5. Once that's done, go to the Applications folder, right-click Install Mac OS X Lion, and choose Show Package Contents. Inside the Lion app, navigate to Contents > SharedSupport.
6. Double-click InstallESD.dmg inside SharedSupport. It will mount a volume called Mac OS Install ESD
7. Enable hidden files (if you don't know how, download TinkerTool).
6. In Disk Utility, select your new partition you created and click the Restore tab.
7. Drag BaseSystem.dmg from Mac OS Install ESD into the Source box in Disk Utility.
8. Drag your new partition into the Destination box and click Restore.
9. Once it's done, go back inside Mac OS Install ESD and drag the file kernelcache onto the new partition.
10. Go to /System/Installation on Mac OS Install ESD and drag the Packages folder into /System/Installation on the new partition. After you copy it, if there is a Packages alias (it'll be a document icon with a little arrow in a corner) still present in /System/Installation on your new partition, delete the alias.
11. Boot from the new partition and install Lion on your existing Snow Leopard partition.