My first task towards understanding the federal spending is to find websites that might explain it for me. After quite a few fruitless google searches, I stumbled upon a pamphlet(pdf) created by the New York Fed back in 2000. The target audience of the pamphlet was kids which is great because it's explaining things at a level even I can understand.
A lot of the pamphlet is about income and deficit vs surplus etc... The key thing I learned is the two types of federal spending, Mandatory and Discretionary and their differences.
The federal government’s budget contains both mandatory and discretionary elements. Consider, for example, Social Security, which accounts for more than 20 percent of total federal expenditures. (Social Security is a program that taxes people when they are working, and then provides them with income when they retire; it also provides income for workers who become disabled and for the dependents of workers who die.) By law, the government has to pay Social Security benefits to anyone who qualifies for them.
Other examples of mandatory spending are Medicare, Medicaid, benefits to retired civil servants, and interest on the debt that the government has accumulated over the years. (Medicare is a program that pays for health care for the elderly and certain disabled persons, while Medicaid is a joint federal-state program that provides medical assistance to low-income persons.) In contrast, spending on items such as national defense, space exploration, and the FBI is discretionary; the government can do more or less of it, as it decides.
There was a chart accompanying the description, but being from 2000 was quite out of date so I decided to omit it. This is great info, unfortunately I'm not any closer to understanding how much money is being spent on what.