Depending on the particular industry you are researching on, information availability can vary greatly. You will probably need to use a range of information sources and include both quantitative (statistics) and qualitative information (descriptive). A few tips:
Industry classification systems are created to promote data comparability. They are often featured in books, databases, and government websites. NAICS (current version) and SIC (older version) are the most widely used in the U.S., although many sources also have their own systems.
An industry association is established to advocate for the industry and associated companies. They collect and provide unique data/articles/reports. Sometimes these sources are on their websites for free.
To find the industry association websites:
Market research reports databases like Mintel and Passport have information on market size.
However, it's not always easy to find size information on a narrow/niche or emerging markets. When that happens, search for Business Source Premier and LexisNexis to see if the info is mentioned in articles. Search websites of relevant industry associations. Google is great at picking up news, blog posts, and press releases that may mention specific numbers.
You may also need to infer from broader market data and come up with your own estimates. Below are two tutorials on how to size a market: