For example, if you are researching ESPN, parent The Walt Disney Company's 2017 Annual Report contains "estimated subscribers (in millions)" on pg. 2. Company Annual Reports, which also contain financials, can be found in the Investor Relations section of the company's website.
If you don't know who owns the network, you might find the answer in a report from the Federal Communications Commission (FCC):
Team/League website (e.g. National Football League Record & Fact Book)
Consider: website, streaming, pre/post "shoulder" programming
Team/League website: look for media kits (e.g. 2017 NFL.com Media Kit)