The president of the United States signs all bills that become laws. Proposed laws are written by members of Congress. The presiding officer of the House or Senate refers the bill to the appropriate committee. If the bill emerges from the committee, it is put to a vote.
When the bill passes one house of Congress, it is passed to the other where it is debated and possibly amended. If the other house passes a different version of the bill, both houses meet to reconcile the differences in a Conference Committee. Once they agree on a new version, it is forwarded to the president, who can choose to either sign or veto it.