World Wide Web search engines are essential tools for efficiently utilising the information on the Web. However, there are certain problems in their use. In particular, users with little experience have difficulties with the search process, which puts them at a clear disadvantage in a world, where more and more information is to be found only on the Web. In this thesis, the focus is on the strategies employed by users of search engines during three phases of the information search process: query formulation, evaluation of search results, and information re-access. In particular, the aim is to describe the strategies of different user groups: highly experienced Web users, elderly users, and Web users with a couple of years of Web experience. The studies showed that, in general, experience is related to greater search success, which, in turn, is a result of search strategies having evolved towards optimal strategies. Especially in fact-finding tasks, the queries of more experienced users tend to be longer, more precise, and, if not successful, iterated frequently. More experienced users are also more efficient in evaluating the search results. In information re-access, the experienced users are innovative and not completely dependent on the tools specifically designed for information re-access. Surprisingly, even experienced users have misconceptions concerning their primary search engine. The elderly face several challenges with Web search engines, such as not understanding the required language and different functionality provided by the interfaces, as well as problems with text input. The thesis presents several design suggestions to place the benefits of successful strategies at the disposal of all users, as well as to make it easier for users to understand the functioning of search engines. For example, the thesis presents a novel, more efficient style for presenting textual result summaries, a natural-language explanation tool for queries, a search interface specifically designed for elderly users, and several ideas for facilitating information re-access. In addition to design ideas, the thesis presents a search success metric that combines search effectiveness and efficiency in a single measurement, called task completion speed.