We study the one-dimensional spin-1 2 Heisenberg model with antiferromagnetic nearest-neighbor J 1 and next-nearest-neighbor J 2 exchange couplings in magnetic field h. With varying dimensionless parameters J 2 / J 1 and h / J 1 , the ground state of the model exhibits several phases including three gapped phases ͑dimer, 1/3-magnetization plateau, and fully polarized phases͒ and four types of gapless Tomonaga-Luttinger liquid ͑TLL͒ phases which we dub TLL1, TLL2, spin-density-wave ͑SDW 2 ͒, and vector chiral phases. From extensive numerical calculations using the density-matrix renormalization-group method, we investigate various ͑multiple-͒spin-correlation functions in detail and determine dominant and subleading correlations in each phase. For the one-component TLLs, i.e., the TLL1, SDW 2 , and vector chiral phases, we fit the numerically obtained correlation functions to those calculated from effective low-energy theories of TLLs and find good agreement between them. The low-energy theory for each critical TLL phase is thus identified, together with TLL parameters which control the exponents of power-law decaying correlation functions. For the TLL2 phase, we develop an effective low-energy theory of two-component TLL consisting of two free bosons ͑central charge c =1+1͒, which explains numerical results of entanglement entropy and Friedel oscillations of local magnetization. Implications of our results to possible magnetic phase transitions in real quasi-onedimensional compounds are also discussed.