If you're trying to depart from Hong Kong during the protests, our first recommendation would be to contact the airline, and ask them if it is possible to reroute your flight from Shenzhen airport.
Hong Kong is so small that it is only served by one airport: Hong Kong International Airport. There is one upside to all of this: It also means that it is more than entirely possible to leave Hong Kong by foot, and catch a flight out from mainland China.
Travelers have flown into neighboring Shenzhen for decades, when flying into Hong Kong airport was cost-prohibitive, often then catching the train or ferry over to the island.
The flights that seem to be the most affected are departures in the afternoon, when the majority of the international flights commence. It seems flights are being allowed to land in Hong Kong; though some flights have been diverted.
For those planning to transit through the airport, please contact the airline about rerouting the flight.
Key city officials are looking to move displaced passengers. From the South China Morning Post this morning:
The Civil Aviation Administration of China on Tuesday announced arrangements to help travelers between Hong Kong and mainland China, by boosting airlines’ capacity and handling ticket transfers and refunds. It added it would increase transfer capacity at other airports in southern China.
The national flag carrier Air China said it would add extra flights between Beijing and Shenzhen, the mainland city neighboring Hong Kong, for the rest of the day.
From ShenzhenIt is possible to get to Shenzhen by MTR or ferry (it will take an hour or two). The main thing is that it will likely require a visa, but there is Shenzhen 5-day special economic visa on arrival available to certain nationalities. These include the U.S., UK, Canada, French, Australia, Germany, Korea, New Zealand, Poland, Romania, Spain, Sweden, and Switzerland.
The cost of the visa is ¥168 ($23.76 USD).
Please note the cost and the list of nationalities that are available for the visa can change. Back in my day, it was not available for Americans, but this information seems to be up to date as so far as we can tell.
SCMP is also reporting that most transit systems (subway, train, bus) to the airport are operating normally, though the Airport Express is operating every 15 minutes (as opposed to the normal 10 minutes). For other ways to get to the airport, check out our Hong Kong guide.
If you plan on continuing to depart from Hong Kong airport, it might even be several days, if not a week or two out, before things return to normal. The protests may go on for a few days, and this is one of those wait-and-see type of situations. You will have better luck and chance getting out if you're able to reroute the itinerary from mainland China.
In terms of cost, this is a great time to check that insurance policy, and check to see if the credit card has any allowances for delays and cancellations. Besides, consider how much more expensive it is to shell out for overnight hotels per night being stuck in Hong Kong.