We present measurements of absolute branching fractions of hadronic and leptonic Ds+ decays to K- K+ pi+, anti-K0 K+, eta pi+, mu+ nu_mu and tau+ nu_tau and report a search for the leptonic Ds+ to e+ nu_e decays. The results are obtained from a data sample of 913 fb^-1 collected at or near the Y(4S) and Y(5S) resonances with the Belle detector at the KEKB asymmetric-energy e+e- collider. The branching fractions of hadronic decays are measured to be Br(Ds+ -> K- K+ pi+) = (5.06 +- 0.15 +- 0.21)%, Br(Ds+ -> anti-K0 K+) = (2.95 +- 0.11 +- 0.09)%, and Br(Ds+ -> eta pi+) = (1.82 +- 0.14 +- 0.07)%, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions of leptonic decays are measured to be Br(Ds+ -> mu+ nu_mu) = (0.531 +- 0.028 +- 0.020)%, and Br(Ds+ -> tau+ nu_tau) = (5.70 +- 0.21 +0.31-0.30)%, which are combined to determine the Ds+ meson decay constant f_Ds = (255.5 +- 4.2 +- 5.1) MeV. We find no significant signal for Ds+ -> e+ nu_e decays and set an upper limit of Br(Ds+ -> e+ nu_e) < 1.0 (0.83) x 10^-4 at 95% (90%) confidence level.