Taking the bus from Ben Gurion Airport to Jerusalem Central Station (or vice versa) is cheap but slow. The Egged shuttle bus, Lines 5 and 5a (fare NIS 5, Israel shekels only), takes 10 minutes to the El Al Junction on Route 40, just outside the airport. Connect to Egged bus, Line 947 (fare NIS 21.50) to Jerusalem's Central Bus Station. A much easier, but sometimes tedious, alternative is a 10-seat sherut taxi (limo-van), run by Nesher. They depart from Ben Gurion Airport (outside Terminal 3) as soon as they fill up, and drop you at any Jerusalem address for NIS 64.
Intercity buses travel all over the country from the Central Bus Station, with frequent departures on more popular routes. A few (like Eilat) require prebooking, which can be done online at www.egged.co.il.
Egged also operates the extensive bus service within Jerusalem. The fare is NIS 5.90, and you don’t need exact change. If you have several days in Jerusalem, consider a Rav Kav card, available at the Central Bus Station, which is good for travel on buses and the light-rail, and allows for transfers between them within a 90-minute period. Extra credit on the card can be bought from bus drivers but not on the train.