Brian, the general expectation is "Article 50" will be triggered before Christmas, but no one truly knows just at the moment.
http://www.telegraph.co.uk/news/2016/07/16/cabinet-clash-over-date-to-trigger-article-50-and-brexit-talks/
I'm not sure if we can complete any other trade deals during the two years negotiation period with the EU. It's certainly against EU law for us to complete any before we give notice. I suspect no one even considered this situation before so it's likely to be a grey area.
We all have to hope that May's government uses any grey areas like this to our advantage, because we undoubtedly have a stronger negotiating hand than the EU, and it's difficult to see what they could do about it even if we did start to write our own rules. They are victims of their own arrogance, because they truly believed that no country would have the financial means or the guts to tear itself away from the EU dependency culture. Once we are out they will certainly revise the exit procedure to try to make it a lot more difficult for other nations to leave.