This is a non binding referendum, so nothing HAS to happen at all. But all the party leaders have promised to abide by the result, with varying definitions of "immediately."

Once the PM formally starts the process, it must be completed in 2 years according to the Lisbon treaty. The end of that period is when the trade deals expire. There will clearly be preparation before they formally pull the trigger, but it's anybody's guess just how long it will be. There may be a change in UK leadership over this, and there are upcoming elections in France and Germany to consider. The Leave campaign has talked about 2020 as a good date to end the separation.

For all the treaties that will expire, trade will fall back to the WTO rules, which (to my understanding) are like the benches at train stations. They're arguably better than nothing, but very uncomfortable to sit on for any length of time.

IMO the market to watch is finance. Losing the free movement of money is an enormous blow to London as a global financial hub. Especially since the London and European stock exchanges are merging, it's possible the big investment banks will simply move to Frankfurt. The financial sector contributes 84bn to GDP (of 2.8tn), so there's a lot at risk there. So if any treaties get signed quick, it'll be the financial ones.