The most common way to get from the airport to Mayanot in Jerusalem is by Super Shuttle, called a Sherut in Hebrew. The Sherut service at Ben Gurion airport is operated by a company called Nesher and are available 24 hours a day to major cities such as Jerusalem and Tel Aviv. They can easily be found just outside the main arrival terminal. The cost per person is approximately $15.00 USD. The other more expensive option is to take a private taxi to Jerusalem.
Another option – There is a bus, #485 to Jerusalem that leaves on the hour, leaving from the second floor. You then take a taxi (or #18 bus ) from the central bus station. Bus costs 17 shekels – taxi from the central bus station would be about about 35 shekels.
There is also a new option – train. It runs every half hour. They are currently on a temporary schedule so please check at the ticket counter. It takes you to the central bus station in Jerusalem from where you would taxi or bus to Mayanot.