The Process:

Introduction Of A Bill (A Draft of Proposed Legislation)

A bill is introduced by a sponsor(s) in one or both houses of Congress.  A bill is assigned a bill number (H.R. 14, 107th Cong., 1st Sess. (2001)).  This bill number usually follows the proposed legislation through hearings, amendments, congressional committees, etc., until enactment or the end of the current legislative period.  A companion bill may be introduced in the other house of the legislature at any time.

Passed By Both Houses Of Congress

1. Committee hearings may be held and committee reports may be issued before being sent to the full house for debate and vote with or without recommendations.  Bill may die in committee and never reach the full house for vote. 
2. When the bill passes one house, it is sent to the other house for consideration.  The other house may approve and pass the bill to the president in identical form.  More likely, the other house will propose a variation of the bill and both houses must negotiate a compromise.
   1. Engrossed Bill.  Passed by one chamber, with amendments.
   2. Enrolled Bill.  Final version passed by both chambers and sent to the President. 

Signed By President Or President's Veto Is Overridden

When both houses pass the bill in identical form, it is sent to the president for a signature or veto.

Becomes A "Session Law" Or "Public Law"

1. If signed (or not vetoed within 10 days), the bill becomes   a “session law” or “public law.” 
2. If  the president vetoes the bill, the veto may be overridden by two-thirds majority in both houses. (If the president takes no activity on the bill at the end of a legislative session  the bill is, in effect, vetoed. This is called a “pocket veto.”)