Note: Check the date the bill was introduced. If you're trying to track current legislation, make sure the bill was introduced in this session, this year. (Sessions are two years long.) If it's from a previous year or session, it is likely "dead."
Check political news and blogs for information on upcoming legislation and policy.
Researching the Bill
Congressional bills generate a lot of documents, such as committee markups, budget estimates, hearings, etc. You can learn a lot from them.
Search news sources for coverage of the bill, the names of the politicians sponsoring the bill, public reaction to the bill, etc.
Search by the bill name ("Affordable Care Act"), number (H.R. 3590), or any popular terms used to refer to the bill ("Obamacare")
Look for news coverage of and opinion about the social problem the bill seeks to address (i.e., "uninsured")
Look out for the names of interest groups, professional associations, or think tanks in these sources. Search for and visit their sites to find their take on proposed legislation and policy issues. Keep an eye out for organizational bias, and consider opinions from different groups (i.e., U.S. Chamber of Commerce vs. insurers' perspectives on the Affordable Care Act employer mandate.)
For federal legislation, check for a Congressional Research Service report on the underlying issue at the Library of Congress, everycrsreport.com (not really every report), which allows you to browse by category, or ProQuest Congressional, which has a deeper archive. The CRS is non partisan and creates research reports for members of Congress on just about everything.
Look at this summary of the previous Congress to give you an idea of what has important in previous Congresses which would affect current legislation.
Also, the Almanac of American Politics is a great resource for doing background research. It summarizes the federal and state level legislative priorities from the previous year.