Parliament will honor the referendum, but not enact Article 50. They will allow more short term losses before holding an "emergency" meeting. They will present a list of demands to the EU which, if approved, will change their minds about leaving. If the EU approves, they will remain in the EU under better terms for them. If the terms aren't approved, let world markets suffer, it will be on the EU failing to accommodate their unique needs.
When something like BREXIT happens it effect that stock market. Those who are in the stock market need to look over their over all portfolio. That's not to say get out, because this is pressing the panic button, which unfortunately some have already done causing the existing issues. No it's time to look things over maybe even talk to a broker to see what action if any should be done.
Successful investors in the stock market should be long-term, diversified investors that do not take a whole lot of risks. There has been a lot of market volatility given the results from the "Brexit" vote. Therefore, investors would be wise to adjust their portfolios to ensure that they are not over exposed to certain markets.
The worst thing that non-professional traders could possibly do would be to reactively adjust their portfolio based on immediate market reactions to Brexit. Although there is potential for full time traders to make money off a "dead cat" drop in the markets, in many cases people changing their portfolio in uncertain times just causes proliferation of losses.