To find scholarly journal articles on a topic, you use research databases that are organized by subject areas. Some of these databases contain the articles online, others (indexes) just have citations.
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Library Databases:

Alt-PressWatch
Full text database of newspapers, magazines and journals of the alternative and independent press. Provides a valuable new source of coverage, viewpoints and perspectives to complement and challenge the coverage of the mainstream media.

Bibliography of Asian Studies
Index to citations on humanities, social sciences, medicine, geology, and the environment as they relate to the East, Southeast, and South Asia.

Academic Search Complete
Database covers all subject areas broadly, though none exhaustively. Includes both popular magazines and scholarly journals, with a large number of full-text articles.

GenderWatch
A full text database of publications that focus on the impact of gender across a broad spectrum of subject areas.

Historical Abstracts
Covers non-US history. It is best for history from 1450 to the present, but includes some medieval sources.

IIMP Full text (International Index to Music Periodicals)
Indexes approximately 400 music periodicals; 52 titles are available with the full text of articles (1996- ).

Index Islamicus
Covers all aspects of Muslim life, past and present. Subject areas include Arabic studies, archaeology, architecture, arts, economics, education, geography, history, law, philosophy, politics, religion, sciences, social sciences, and theology.

JSTOR
Full-text, scholarly articles online on the social sciences, humanities and various sciences subject areas.

Periodicals Archive Online
Full-text articles online from N. American & European scholarly journals in the arts, humanities and social sciences.

Project Muse
Online, full-text scholarly articles in the arts, humanities, social sciences and mathematics.

Sociological Abstracts
Journal articles online/full-text mainly on sociological/psychological issues such as gender, race, identity, nationalism, and religion.

Worldwide Political Science Abstracts
Research within the political science discipline and its complementary fields, including international relations, law, and public administration/policy.