Installing IE 6 cannot be done in Windows 7 Directly and if there were some hack to do so, I wouldn't recommend relying on it to present appropriately.
While you can use Virtual Box, VMWare, or some other virtualization product, the best option from a cost perspective is almost certainly to use XP Mode which is a pre-built XP Virtual Machine provided by Microsoft. XP Mode requires you have Windows 7 Pro, Enterprise, or Ultimate. If you don't have Windows 7 Pro, upgrading to Pro is the cheapest way of doing this - using the Windows Anytime Upgrade, it costs about $90 to go to Pro. Otherwise, you'd have to purchase a full retail copy of Windows 7 (or find an old full retail copy of XP) if you don't have one lying around. Such a copy would likely cost you close to $300.