Most likely, the word "free" in "free government grants" is a mistake. If you're lucky, you can get a grant for free, but you have to put in a lot of time, work, and money to get one. Your proposal needs to be written by an expert, and most organisations either have someone like this on staff or have to pay for expensive services. Even if your proposal is really good, you can't be sure that you will get the money. Also, you will have to pay someone to manage how the grant money is spent according to the proposal. If you don't, you could be fined.
Let's look at where money comes from in the first place. Congress is where everything starts and ends. Here, laws are made and decisions are made about how much money needs to be spent. These funds are given to the different government agencies so they can pay for big projects. How much money goes to each programme is up to Congress to decide. Anyone or any group can apply for one of these grants.
Once these funds are approved in the federal budget, they are written about in the Federal Register. The CFDA, or Catalog for Federal Domestic Assistance, lists the programmes that have been approved. Their website is at http://www.cfda.gov/. All of it is free, and you can look for programmes online where you can make your applications. On the site, you can find information about how to use the grant money, how to apply, and how the review and funding process works.
You can fill out applications for programmes that are related to your projects online. Congress gave $20 million to the Department of Health to help stop cancer. If you or your organisation are working on a project related to this, you can apply for funding.
You can also ask different federal agencies for money. Go to their websites and look at the different government agencies to see if you qualify for a free government grant application.
You can apply for Federal Pell Grants if you are a student. Or, you could send them your application for free grants. Check to see if you can join their programmes. How much money you get will depend on how much you need. This would depend on how much school costs, if you are a full-time or part-time student, and if you plan to stay for the whole school year or not.
You can also apply for student aid programmes that are based on campus. This will also give you money based on what you need. FAFSA, which stands for Free Application for Federal Student Aid, can also be used to apply for other types of student aid. You can do this on their website, http://www.fafsa.ed.gov/. Make sure you don't miss your chance to get this free grant from the government.