Computational argumentation is expected to play a critical role in the future of web search. To make this happen, many search-related questions must be revisited, such as how people query for arguments, how to mine arguments from the web, or how to rank them. In this paper, we develop an argument search framework for studying these and further questions. The framework allows for the composition of approaches to acquiring, mining, assessing, indexing, querying, retrieving, ranking, and presenting arguments while relying on standard infrastructure and interfaces. Based on the framework, we build a prototype search engine, called args, that relies on an initial, freely accessible index of nearly 300k arguments crawled from reliable web resources. The framework and the argument search engine are intended as an environment for collaborative research on computational argumentation and its practical evaluation.