Actually, that's the service provided by GS, etc. They have those buyers on the other side of their Rolodex.
Well, yes. They're the ones who actually employ the hundred lawyers and PR staff. But that's what it takes, and it's not about clicking some buttons on a Web 2.0 Day Trading UI.
It's really not far from it. You don't need to do a private off-exchange sale (though you can), they do incremental execution (where you break the trade in small batches)
What is GS?
a great vampire squid wrapped around the face of humanity, relentlessly jamming its blood funnel into anything that smells like money
Goldman Sachs