Getting here by car
If you have a car, you should drive towards Beer-Sheva and then go south on road number 40. After the junction with road number 204, you will reach Kibuttz Sde Boker. Keep on for a little more and then turn left to Midreshet Ben-Gurion. You should see signs for "Ben-Gurion's Grave" and "Ein Avdat".
Getting here by bus
In order to come here by bus, you should first go to Beer-Sheva. Take line number 370, from the Tel-Aviv central bus station. If you come from Jerusalem, you should take bus number 446 or 470. From Beer-Sheva you should take the bus to Mizpe-Ramon, it's bus number 060 or number 392. If it's Sunday morning, you can take bus number 395 directly from Tel-Aviv at 9:00.
Ask the driver to drop you at Kever Ben-Gurion (Ben-Gurion's grave). The grave is located a little south to kibuttz Sde Boker, near Midreshet Ben-Gurion.
From here you'll need to go down by foot until you get to the entrance to Ein Avdat. Before starting to go down, you should pay the entrance fee. They will give you any information you might need.