For maximum safety you can dig about 50 cm (20") in the ground, but even the half of that would do. The concrete-filled holes can be about 10"-15" (30 cm) in diameter. You can calculate the volume easy - (2 * 30 * 3.14) * 50 = 35357 cubic cm. That's not much.
I could not find exact instructions on digging the holes but this porch swing guide has quite detailed instructions and on this article about metal swing sets you'll find some more general information.
