Well Grumpy, I wish I was still cleaning up PCs en mass. I had a nice gig doing so and now I don't touch them often so I lost a lot of up-to-date knowledge.
WallJump, Here is the standard process for PC shops.
Download all the respectable Free and trial bits of antivirus softwares and Antispyware applications. NONE of them will clear 100% so it is often required to use a handful. The shop I ran used 8 anti-spyware tools for removal as standard.
<--- The IE process can be traced with a tool call process explorer.---> http://technet.microsoft.com/en-us/sysinternals/bb896653
This will get you an idea towards what is causing the process to launch, who is the owner, and what files are associated with it. After that, there are other tools to go further, but as you do, the complexity increases and its hard to really give lessons via forum.