Consider the atom as a two level system comprising a ground state and an excited state. The atom is excited by photons of a particular wavelength; furthermore, each photon gives the atom a momentum kick in the direction of the light and with a magnitude of Planck's constant h divided by the wavelength of the light. This results in a change of velocity of about a few mm per second, but for strong atomic transitions we can scatter 10**7 photons per second, giving a deceleration of about 10**4 times g, the local acceleration due to gravity. Six laser beams are arranged othogonally in opposing pairs, one of each pair right circularly polarized, the other left. The lasers are detuned to a longer wavelength than that of the transition ("red" detuning), so that an atom approaching the light will come into resonance by virtue of the Doppler effect and hence receive a momentum kick opposing its motion. This results in a damping force. Where the orthogonal beams intersect is also the center of an inhomogeneous magnetic field created by two wire coils in an anti-Helmholtz configuration (i.e., with the current of one coil going in the opposite direction of the current in the other). The magnetic field causes an imbalance in the radiation pressure for atoms displaced from the center of the trap, pushing the atoms back toward the center. This is the restoring force. Without the magnetic field there is no trap but rather what is called optical molasses.
In our (rubidium) traps we use the 5S1/2 F=3 to 5P3/2 F=4 transition for our cooling lasers; this is at 780 nm. What often happens to atoms relaxing from that excited state is that they sometimes decay to the other (F=2) ground state, which is not affected by the cooling laser. Eventually (which in human time scales means very quickly) all of the atoms wind up there in a process called optical pumping. To counteract this we "repump" the atoms to a 5P hyperfine state where it is more likely that they will decay to the correct (F=3) ground state. The LVIS experiment uses 780 nm light to repump them into a 5P3/2 state, while the cell trap experiment uses 795 nm light to drive the 5S1/2 F=2 -> 5P1/2 F'=3 transition. (These are for the 85Rb isotope. Slightly different hyperfine states are used with the 87Rb isotope.)
For a more advanced description a good source is "Inexpensive Laser Cooling and Trapping Experiment for Undergraduate Laboratories" by Wieman, Flowers & Gilbert, published in the American Journal of Physics, April 1995, pp.317-330. Its brief bibliography is excellent. Other papers on a somewhat-advanced- but- not-yet-specialist level are "Cooling and Trapping Atoms" by Phillips & Metcalf in Scientific American, March 1987, pp.50-56, and "New Mechanisms for Laser Cooling" by Cohen-Tannoudji & Phillips in Physics Today, Oct. 1990, pp.33-40.