We analyze the bubble-formation process that occurs when there is phase coexistence in the early Universe. In this paper we stress the relevance of determining the surface tension in order to compute some quantities that are relevent to cosmology such as the number density of bubbles, the contrast density, and the most probable sizes of bubbles (critical radius). We show how these quantities can be expressed as a function of the surface tension. We propose a method for computing this thermodynamical variable. The surface tension is shown to acquire a very simple dependence in the high-temperature limit and can be easily predicted up to the one-loop approximation.