It's essentially done with robotic pipettes, though the ones used in DNA synthesis are very specialized.

It can be done with hand pipettes, but it would be a slow and error prone process.

The materials are not exotic and can be purchased from chemical supply.

Typically the starting material is a (population of) a single DNA (or RNA) base bonded to a glass bead (cpg), and the chemistry is done by washing the beads with a series of chemicals, following a repeated recipe. The recipe is identical for each base added to the chain (excepting the base itself of course).