The government really doesn't offer people free money so there really is no way to get free money from the government but there are some scams going around on the internet or through phone calls saying you have won a free government grant which are scams.
You can get help from the government though to pay for utility bills, free cell phones, Educational Grants, and free healthcare for your child.
You can make money online by blogging, selling T Shirts, Taking Surveys online for money, Typing At Home Jobs etc.