A federal law is a law passed by the United States government, or federal government. Federal laws are supreme over state laws (only in the case of the enumerated powers, states are able to pass laws concerning all other matters).
Federal laws start as bills in one of either the House of Representatives or Senate. For bills starting in the House, the bill goes through committee, where it is refined, then passed on to the House Rules Committee in which parameters are set for its debate on the House floor. Once there, it is debated, then voted upon.
If passed, the bill then enters the Senate, where it passes through committee, then to the floor. In the Senate, filibusters may be used to defeat the bill. If 60 Senators vote for cloture, a filibusteer must cease, and speaking is limited to an hour per Senator. After this time limit expires, the bill is voted upon.
If passed, the bill enters a conference committee composed of members from the relevant House and Senate committees. As the bill has usually been changed during its trip through each house, the conference committee compromises on any discrepancies in their respective bills. After the compromise is made, the bill must be passed by both houses again, but may not be edited.
If passed again, the bill goes to the President to be signed or vetoed. A vetoed bill is returned to Congress, which can overturn the veto with a 2/3rds vote from each house. If the president does not sign or veto the bill in ten days, it is passed into law unless Congress has adjourned during the ten-day period. The bill would then be pocked vetoed.
When a Federal law is broken it is called a Federal offense, suspects are investigated and arrested by the Federal Bureau of Investigation, and tried in a Federal Court.