Conversational search has evolved as a new information retrieval paradigm, marking a shift from traditional search systems towards interactive dialogues with intelligent search agents. This change especially affects exploratory information-seeking contexts, where conversational search systems can guide the discovery of unfamiliar domains. In these scenarios, users find it often difficult to express their information goals due to insufficient background knowledge. Conversational interfaces can provide assistance by eliciting information needs and narrowing down the search space. However, due to the complexity of information-seeking behavior, the design of conversational interfaces for retrieving information remains a great challenge. Although prior work has employed user studies to empirically ground the system design, most existing studies are limited to well-defined search tasks or known domains, thus being less exploratory in nature. Therefore, we conducted a laboratory study to investigate open-ended search behavior for navigation through unknown information landscapes. The study comprised of 26 participants who were restricted in their search to a text chat interface. Based on the collected dialogue transcripts, we applied statistical analyses and process mining techniques to uncover general information-seeking patterns across five different domains. We not only identify core dialogue acts and their interrelations that enable users to discover domain knowledge, but also derive design suggestions for conversational search systems.