Exact closed-form expressions for the electromagnetic induction fields produced by vertical and horizontal current sources in the conducting ocean overlying a one-dimensional earth are derived from the Maxwell equations. Numerical methods for the evaluation of the solutions are given, including correction for the finite size of real sources. Simple models of the electrical conductivity structure of the ocean crust and lithosphere are deduced from geologic, petrologic, and laboratory data, and their electromagnetic response is modeled. Horizontal electric dipole sources produce much larger field amplitudes than their vertical counterparts for a given frequency and range, and the horizontal electric field offers superior received signal performance. Reflections of electromagnetic waves from the sea surface and thermocline must be considered for low enough frequencies or long ranges. Estimates of the ambient noise level from natural electromagnetic sources in the frequency range 0.01--10 Hz are presented. The ability of controlled sources to determine features of the conductivity of the ocean crust and upper mantle, especially low conductivity zones, is demonstrated. If the mantle conductivity is low enough, horizontal ranges of 50 km and conductivity estimates to over 20 km depth can be achieved.