We study the phase transitions of interacting bosons at zero temperature between superfluid ͑SF͒ and supersolid ͑SS͒ states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard ͑X͒ and collinear ͑C͒, which are the simplest cases arising in two dimensions on a square lattice. We find that the SF-CSS transition is in the three-dimensional XY universality class. The SF-XSS transition exhibits nontrivial critical behavior, and appears, within a dϭ3Ϫ⑀ expansion, to be driven generically first order by fluctuations. However, within a one-loop calculation directly in dϭ2 a strong-coupling fixed point with striking ''non-Bose-liquid'' behavior is found. At special isolated multicritical points of particle-hole symmetry, the system falls into the three-dimensional Ising universality class.