The absolute branching fractions for the decays D{sub s}{sup -} {yields} {ell}{sup -}{bar {nu}}{sub {ell}} ({ell} = e, {mu}, or {tau}) are measured using a data sample corresponding to an integrated luminosity of 521 fb{sup -1} collected at center of mass energies near 10.58 GeV with the BABAR detector at the PEPII e{sup +}e{sup -} collider at SLAC. The number of D{sub s}{sup -} mesons is determined by reconstructing the recoiling system DKX{gamma} in events of the type e{sup +}e{sup -} {yields} DKXD*{sub s}{sup -}, where D*{sub s}{sup -} {yields} D{sub s}{sup -} {gamma} and X represents additional pions from fragmentation. The D{sub s}{sup -} {yields} {ell}{sup -}{nu}{sub {ell}} events are detected by full or partial reconstruction of the recoiling system DKX{gamma}{ell}. The following results are obtained: {Beta}(D{sub s}{sup -} {yields} {mu}{sup -}{nu}) = (6.02 {+-} 0.38 {+-} 0.34) x 10{sup -3}, {Beta}(D{sub s}{sup -} {yields} {tau}{sup -}{nu}) = (5.00 {+-} 0.35 {+-} 0.49) x 10{sup -2}, and B(D{sub s}{sup -} {yields} e{sup -}{nu}) < 2.8 x 10{sup -4} at 90% C.L., where the first uncertainty is statistical and the second is systematic. The branching fraction measurements are combined to determine the D{sub s}{sup -} decay constant f{sub D{sub s}} …