If you want to do a clean installation of Lion (or you want to install it on a Hackintosh), you'll need to install it on some sort of physical media, which Apple doesn't yet provide. Luckily, it's very easy to burn Apple's installer to a DVD or flash drive:
- Download Lion from the Mac App Store. The installer should show up in your Applications folder.
- Right-click on the installer and hit "Show Package Contents". Navigate to Contents > SharedSupport and look for a file called "InstallESD.dmg".
- Open up Disk Utility and drag the DMG file into the left-hand sidebar. If you're burning it to a DVD, insert your DVD, select the disk image in the sidebar, and hit the "Burn" button. Skip down to the last step to use it.
- If you want to burn Lion to a USB flash drive, plug it in and click on it in the left-hand sidebar in Disk Utility. Go to the Partition tab and select "1 Partition" from the dropdown menu. Choose "Mac OS Extended (Journaled) on the left.
- Hit the Options button under the partition table and choose "GUID Partition Table". You'll need this to make the drive bootable on a Mac. Hit the Apply button when you're done to format your drive (note: it will erase everything on the drive).
- Click on the "Restore" tab, choose the InstallESD.dmg file as the source and your flash drive as the destination. Hit the Apply button and it will create your bootable USB drive.
- Reboot into OS X and hold the option key when you hear the startup chime. You can boot into your DVD or flash drive from there.
You'll not only be able to install Lion from this drive, but you'll also be able to use Disk Utiltiy, recover from a Time Machine backup, and do everything else you could do with the old installation DVDs. Note that when you install Lion, it'll create a recovery partition with all these features anyway, so you don't need the DVD unless you're doing a clean install. Though it's always nice to have around in case something happens, like you erase your entire drive. Not that that's ever happened to me three times in one week or anything.