In academic writing, you must refer to your sources and cite them correctly. The demands may vary between different studies and fields, so “correctly” in this context is a very broad concept. Some use name/year in parenthesis, others use numbers in parenthesis, some use numbers superscripted, others use name/year in the footnote system.
There are many different citation styles: APA, MLA and Vancouver are just a few. Each academic field has its own preferences, and there is often an academic organisation behind a style. For instance, health studies tend to follow the NLM or Vancouver style, while interdisciplinary fields in the humanities or social studies tend to use the APA or Harvard.
If you need help with a specific style, you can find guides or tutorials on the web, but be sure to check the original sources. Below you can get an overview over the many styles you can choose from, and which fields of research they belong to. Ask your supervisor, if you are in doubt about which one to choose.