This is the first in a series of papers concerning the electrical and thermal transport properties of dense plasmas. Temperatures and densities considered range approximately from room temperature to ${10}^{4}$ eV and from ${10}^{\mathrm{\ensuremath{-}}4}$ to ${10}^{4}$ times compressed. In the present work we describe theoretical calculations of electrical conductivities using the t-matrix version of the Ziman theory with various self-consistent ionic potential models and realistic structure factors. The theoretical basis is described, and illustrative results are given.