The actual signing of papers? It depends on the laws where you live. I have had the sellers sign papers in the morning and we as buyers signed in the afternoon. We sold a house last year and it took three days. We signed the papers and the buyers signed three days later. That was to cover the 72 hour law to back out of a contract.
As for setting a closing date that is flexible. We have always set it for 30 days or less.
It will all depend on the place you live. Your closing date is usually specified in the purchase agreement that both the buyer and seller agree to. However, if all the papers are in order, you can close within three weeks to 1 month. You can check out http://homebuying.about.com/od/buyingahome/qt/101107_homclose.htm for more information.