The best way is to take No. 327 Airport Express to Window of the World and take the subway all the way to Luohu station

It will depend on how well do you know Shenzheen and also how much of a risk to get lost you are willing to take.  The safest way is to go by taxi ( but not the cheapest), but there are multiple other choices and combinations of them, including buses and even ferries.  Of course, it will depend if you just go to border and back, or if you will continue to Hong Kong.

Best and cheapest way is to take the bus from outside the arrivals gate in Shenzhen airport. Interesting onboard video will ask passengers not to smoke, walk, or diet while on board. Bus will make 3 other stops before arriving close to the border and cost is 20 rmb - do not pay ticket check girls, they will rob you blind, buy your ticket from the ticket office.  On arriving in Shenzhen, there will be plenty of local bang-bang workers there offering to carry your case to the crossing point. I suggest that you choose one but the going rate is 10 rmb and it's a 10 minute walk to the check point into Hong Kong. Don't pay more than 10 rmb.

the subway runs all the way and costs like 9 yuan and takes about 65 minutes