When viewed as a classical electromagnetic wave reflecting from a surface, the delay is zero. Looking at it in more detail, you can think of it as a classical wave striking a bunch of free electrons and there is no "surface". The electrons are accelerated and decelerated by the field and so they emit an electromagnetic wave of their own, and this process takes time. As you go further into the body of the reflector, the wave is shielded by these electrons and after a certain small distance, the impinging wave is practically absent. The wave from an oscillating electron will interfere with the waves from other electrons, and only very near an angle of reflection equal to the angle of incidence will their waves interfere constructively, as long as the dimensions of the reflector are large compared to the wavelength of the incoming radiation. The full answer is given in quantum electrodynamics, where an incoming photon is absorbed by an electron, which then emits a photon in a more or less random direction. The incoming photon rarely gets very far into the material, but the absorption and emission process take a small amount of time. Again, only very near an angle of reflection equal to the angle of incidence will the wave function of the photons interfere constructively, as long as the dimensions of the reflector are large compared to the wavelength of the incoming radiation.