The absolute branching fractions for the decays D(s)(-) -> l(-) (nu) over bar (l) (l = e, mu, or tau) are measured using a data sample corresponding to an integrated luminosity of 521 fb(-1) collected at center-of-mass energies near 10.58 GeV with the BABAR detector at the PEP-II e(+)e(-) collider at SLAC. The number of D(s)(-) mesons is determined by reconstructing the recoiling system DKX gamma in events of the type e(+)e(-) -> DKXD(s)*(-), where D(s)*(-) -> D(s)(-) gamma and X represents additional pions from fragmentation. The D(s)(-) -> l(-) nu(l) events are detected by full or partial reconstruction of the recoiling system DKX gamma l. The branching fraction measurements are combined to determine the D(s)(-) decay constant f(Ds) (258.6 +/- 6.4 +/- 7:5) MeV, where the first uncertainty is statistical and the second is systematic.