How to get to Ben Gurion Airport
Getting to Ben Gurion Airport from Jerusalem is a bit complicated, though heading in the other direction is so easy with sherut.
I, the author, have got there with two different ways so far.
In both cases, you’ll have to arrive at Central Bus Station first.

However, I took these transportation in 2012, which means it’s already over 5 years ago. Please check the latest information for making it sure.
1. How to get Central Bus Station in Jerusalem
From Old City to Central Bus Station
20 mins from [City Hall] near Jaffa Gate to [Central Bus Station]: 6.6 NIS (2012).

You may come across ticket inspectors while you are on the tram. Check well your ticket before riding on.

Make sure to have your ticket with you before hopping on.
2-A. From Central Bus Station to Tel Aviv Ben Gurion Airport
2-A-1. Central Bus Station to Tel Aviv Bus Station
1 hour from Central Bus Station by Egged Bus: 22 NIS (2011)
This bus won’t pass the airport but it stops at Tel Aviv Bus Station.
2-A-2. HaHagana Station to Ben Gurion Airport
From Tel Aviv Bus Station, walk to HaHagana train station by walk (400m) to the west.

Ben Gurion train station is just next to HaHagana station. 14 NIS (2011).
You can buy a ticket from a vending machine.

There is a security control before entering to the platform.
2-B. From Central Bus Station to Tel Aviv Ben Gurion Airport
2-B-1. From Central Bus Station to suburb of Ben Gurion Airport
When you ask the bus to Ben Gurion Airport at the ticket counter, they might sell a ticket of a bus which goes through a bus stop near the airport. 1 hour, 24 NIS (2012).

Because the bus stop is on a boulevard and it’s hard to recognize as the stop to get off, ask the driver to tell you when the stop would be reaching.
2-B-2. From the bus stop to Ben Gurion Airport
15 mins with a no.5 local bus which stops in front of arrival floor of the airport: 5.5 NIS (2012)

There is a security control at the entrance of the airport, as usual.
3. Taxi from Jerusalem to Ben Gurion Airport
I’ve never taken a taxi to Ben Gurion Airport, though, some taxi driver offered me once 200 NIS for one way.
I didn’t take it because it was too expensive for one person, but if you are a group, it could be a choice.