Obviously a flight and VIP car service is fast and easy. Both will get you through customs & border control without massive lines and trying to understand chinese without actually knowing it.
Is there a cheaper yet fast way?
I crossed back in 2012 using the Shenzhen metro (I believe it was to Lo Wu/Luohu), then walking across the checkpoint, then taking the MTR train to downtown Hong Kong, just as user Gagravarr mentions in comments. It was super-fast, easy and cheap, no Chinese language knowledge required. I do recommend getting a 1st-class MTR ticket though - it's slightly more expensive but the extra comfort may be worth it (and is definitely worth it if you have lots of luggage).
I've also crossed the other way by train, it was also quick and easy but unfortunately I don't remember the details.
Flying such a short distance sounds horrible - just like user davidvc mentions in comments, there likely aren't direct commercial flights, but even if there were, the hassle of getting to the airport long enough before a flight would likely eat up half your day.
You could probably take a taxi to the checkpoint if you want to avoid Shenzhen metro. Also, looking at http://wikitravel.org/en/Shenzhen , there are tons of options - border-crossing coaches, even ferries, etc.
The answer is a little bit long, so i jump to the conclusion in the beginning.
Louhu/Lo Wu Point is suggested to be used due to its location advantage, and Futian/Lok Ma Chau is also advised. If you are going to HK airport, travel by ship is also a good option. Chartered car are advised if you have enough budget/ travel with disabilities.
There are 6 control points/Kouan(Port) between Shenzhen and HK:
The most convenient way is Louhu/Lo Wu, the port in Shenzhen side is serviced with many public transport including train, metro, local bus and long-route coach services. In HK side it is only linked with metro(MTR).
The downside is that it is very busy. It takes half an hours to enter to HK side and more than an hours on public holidays. Another problem is that the port building in Shenzhen side is poorly designed and maintained.
Futian Kouan and Huanggang Kouan is located closely, around 15mins walk, but their clearing process is quite different. There is metro services to Futian Kouan and both port are serviced by local bus.
Lok Ma Chau Spur Line Control Point is serviced by MTR and a few local bus route, while Lok Ma Chau Control Point is serviced by local bus services to North distinct and directly coach services to Kowloon and Hong Kong Island.
Lok Ma Chau control point is the only port 24hr opened, but the point buildings of Shenzhen and HK are located seperatly, which means you can only access between port by Shuttle bus services called Huangbus (皇巴士) or the direct coach services, and finish the immigration process in 2 separate place.
The 2 ports is less busy than Louhu/Lo Wu but same busy on public holidays. Moreover, the 2 ports in HK side is not linked on foot or by any transport.
Shenzhenwan /Shenzhen Bay port is less used but also less convenient. Both side are serviced with a few bus/coach serviced, and it is far from Shenzhen city centre. The port is also busy on public days but less than the 3 mention above. The remain 2 ports are even less convenient but also less used.
It takes 45mins-1hrs from the port(after immigration and custom control) to Kowloon, and 1-1.5hr to HK Island, regardless by Coach or by MTR.
More details can see here
There is ship services between Shekou Ferry Terminal (蛇口客运码头) and Skypier(海天客運碼頭) within HK airport/Hong Kong - Macau Ferry Terminal (港澳客輪碼頭). Shekou Ferry Terminal is in Hong Kong Island and close to CBD area. It serviced by local bus and metro, while Hong Kong - Macau Ferry Terminal is serviced by Bus, tram and MTR. The time for immigration and custom in the ports is less than land transport, although fares is doubled.
Please noted that passengers are required to have a valid air ticket on the same day if they are going to HK airport, except some condition. The passengers can also finish the flight checkin process in Shekou.
It takes around an hour to Hong Kong - Macau Ferry Terminal and 30mins to HK airport.
There is no scheduled services between Shenzhen airport and Hong Kong airport. It sounds as strange as direct flight between San Francisco and Oakland.(though there is connecting flight between SFO and OAK).Skyshuttle(空中快線) provides chartered helicopter services between Hong Kong - Macau Ferry Terminal and Shenzhen airport.
Many companies provides chartered car services between Shenzhen and HK. The charactered car usually passes though Shenzhenwan port or Huanggang port, depends on final destination. Passengers finish immigration process on the car, and custom process are random checked.
The price vary in terms of passengers, day and time, destination and type of car. My uncle lived in Dongguan often visited to HK by chartered car and it cost around 150RMB per person. You can google the price, but noted that the companies having English website always more expansive.
Shenzhen airport has multiple direct cross-border buses available that will get to to Hong Kong by bus. The most obvious one will be by a company called "China Link" and costs around $100 RMB, and can get you to any major city in Hong Kong with one payment, which gets you a bus ride across the border, and then another to your destination. This company has a big area in the cross border transportation area, has nice seating, and the staff have some level of English. This route is fast (does not cross the border at Louhu/Lo Wu, so it avoids most of the road traffic), but is several times more expensive. Of course, $100 RMB translates to about $15 USD... so that's actually not bad already.
There is also the 330 line that gets you to Louhu/Lo Wu, then you can take the MTR. The 330 line is only $20 RMB, but takes about 1.5 hours to get to Louhu/Lo Wu. The staff is basically non-English, signs are non-English, and you will have to purchase tickets China-style (just hand money at the cashier), but you may encounter problems if you're English only.
There is also "Line 12" which has a stop at the exterior bus station. This bus takes only 1 hour to reach Louhu/Lo Wu, but the bus is less frequent, is harder to find, and the staff are also non-English.