The Earth forms most of its crust at divergent plate boundaries, where two plates move away from each other. The boundary is where magma upwells in a convection current from the mantle, and hardens into brand new crust as it cools. The biggest and most famous place where this is happening is the Mid-Atlantic ridge, and the volcanic islands along it (e.g. Iceland). The other major place is Africa's Rift Valley. In about 10,000 yrs geologists estimate that Lake Victoria will be the south end of a new gulf in the Indian Ocean, as the Horn of Africa pulls away from the rest of Africa.
The rest of the crust comes from the material of other volcanoes. Pyroclastic materials from eruptions, and solidified magma chambers (most granite formations) make the rest of the new crust.