Electrical conductance through various nanocontacts between gold electrodes is studied by using the density functional theory, scalar-relativistic pseudopotentials, generalized gradient approximation for the exchange-correlation energy and the recursion-transfer-matrix method along with channel decomposition. The nanocontact is modeled with pyramidal fcc(100) tips and 1 to 5 gold atoms between the tips. Upon elongation of the contact by adding gold atoms between the tips, the conductance at Fermi energy E(F) evolves from G a parts per thousand 3G(0) to G a parts per thousand 1G(0) (G(0) = 2e/h(2)). Formation of a true one-atom point contact, with G a parts per thousand 1G(0) and only one open channel, requires at least one atom with coordination number 2 in the wire. Tips that share a common vertex atom or tips with touching vertex atoms have three partially open conductance channels at E(F), and the symmetries of the channels are governed by the wave functions of the tips. The long 5-atom contact develops conductance oscillations and conductance gaps in the studied energy range -3 a parts per thousand currency sign E-E(F) a parts per thousand currency sign 5 eV, which reflects oscillations in the local density of electron states in the 5-atom linear "gold molecule" between the electrodes, and a weak coupling of this "molecule" to the tips.