Metasurface analogues of electromagnetically induced transparency (EIT) have been a focus of the nanophotonics field in recent years, due to their ability to produce high-quality factor (Q-factor) resonances. Such resonances are expected to be useful for applications such as low-loss slow-light devices and highly sensitive optical sensors. However, ohmic losses limit the achievable Q-factors in conventional plasmonic EIT metasurfaces to values <~10, significantly hampering device performance. Here we experimentally demonstrate a classical analogue of EIT using all-dielectric silicon-based metasurfaces. Due to extremely low absorption loss and coherent interaction of neighbouring meta-atoms, a Q-factor of 483 is observed, leading to a refractive index sensor with a figure-of-merit of 103. Furthermore, we show that the dielectric metasurfaces can be engineered to confine the optical field in either the silicon resonator or the environment, allowing one to tailor light-matter interaction at the nanoscale.