There are a few possible scenarios.
1) Britain simply leaves the EU and doesn't come to any specific deal on trade between the UK and Europe and either party can impose whatever tariffs and restrictions they want. In this case any goods sold to Europe would still have to conform to CE regulations.
2) Britain stays in the single market. This is a similar situation to the one Norway is in at the moment. Norway pays for access to the EU market and has to abide by most EU regulations, and adopt free movement of people from the Schengen area. It's also worth noting that Norway has less control over immigration from the EU than does the UK (currently).
3) Britain negotiates its own deal. Nobody really knows what this would look like. Free movement of people is likely to be a sticking point as the EU is likely to insist on it but reducing immigration was a key argument of the Leave campaign. It is also hard to see why the EU would accept a deal where the UK makes a smaller net contribution than it does now. The key thing here is that it is a negotiation so the deal could be anything from very similar to the current situation to no agreement at all.
It is also possible that after the the 2 years for negotiation allowed by article 50 no agreement is reached and all of the existing EU treaties simply end and Britain is out without any sort of deal in place. One of the crucial difficulties is that in a modern economy where service industries dominate it is quite difficult to make a rational distinction between movement of goods and movement of labour.
There is also the complication that the EU will place a high priority on stabilizing the remaining membership and discouraging any moves to leave by other members which may well mitigate against giving the UK any special deal that doesn't come with serious strings attached.
It is much more difficult to predict how more general collaboration on things like scientific research, education, culture and security will be affected. Clearly the nature of the eventual arrangements for travel and work will have a significant impact on this.