Do atoms of a surface excite to reflect the light? How do surfaces reflect certain colours and absorb the others?
 A: Short answer: Light is absorbed and re-emitted all the time. Colors and reflectivity all depend on the electrons in the material, and what the material is. Sometimes photons are converted to heat in a material. Other times photons pass through a material or are re-emitted (so it may look like they just "passed through"). Depending on what photons are re-emitted, you'll get varying colors. There is no rule that says electrons must drop down to an energy state they previously occupied, so "weird" things can happen.
More Details: Atoms and the electrons in them have energy levels. Electrons can absorb photons and "jump up" to a higher energy state. Electrons that can "jump down" to lower energy states will eventually do so. The Pauli Exclusion Principle is also important here; if an electron already occupies a state, no electrons can jump up or down to that energy. In bulk materials, the electron energy levels form energy "bands" which basically work similar to energy levels in individual atoms, but with added complications.
When light shines onto a material, every atom the light passes can either absorb the light (if the correct states are available) or not. If the light isn't absorbed, it just passes right through the material like it was not there. If the light is of the correct energy and an electron's potential energy state is available, it is absorbed by an electron, and jumps to another energy level! The electron may jump back down to another energy state, or the energy from the excitement can be made to become heat energy. If the electron jumps down, then the light is re-emitted.
Colors generally arise because the light which hit a material is composed of many different types of light. Certain wavelengths of light are absorbed by a material. Sometimes a material is a color because it "gobbles up" all but a certain color. Other times, a material is a color because it's absorbing a wavelength and the re-emitting photons, sometimes of a totally different wavelength!
Reflections happen because some materials are really bad at converting light's energy into heat and materials can re-emit photons of the same energy. Every time a light ray goes through a medium change, it produces a reflected and a transmitted ray. (On a smaller scale, this is just those surface atoms absorbing and re-emitting photons in a more-or-less random direction.) If you can arrange materials so that the reflected light is more intense than light transmitted from the other side, you'll see a reflection!
A: Light of different color is understood as a wave of different frequency of oscillation. Matter in surfaces has characteristic behaviour for each of these frequencies, based on its chemical composition: electrons in the surface oscillate   and absorb a lot of light when its frequency is around one of resonance frequencies of the matter; and the electrons oscillate less if light frequency is far from their resonance frequencies, and then they transmit and reflect more, depending also on their density and angle of incidence of the wave on the surface.
A: You ask:

Do atoms of a surface excite to reflect the light?

but it's actually the other way round. Reflection occurs because the oscillating electric field of the light produces oscillating dipoles in the electrons in the substrate. These oscillating dipoles in turn radiate light isotropically and the reradiated light interferes constructively only in the directions of transmission and reflection. Note that no energy is lost ion this process - the sum of the reflected and transmitted energies is the same as the incident energy.
However the substrate may have an electronic excitation that matches the wavelength of the incident light. In this case light will be absorbed and excite electrons in the substrate into higher energy levels. In a solid or liquid the excited electrons typically relax by transferring energy to lattice vibrations rather than reradiating light, and the end result is that the light is absorbed and ends up as heat.
So what actually happens is:

Atoms of a surface excite to absorb the light

