When the house or senate passes a bill, it is referred to the other chamber, where it usually follows the same route through committees and finally to the floor. If president doesn't sign the bill within 10 days and congress is not in session, the bill will not become a law.
After both the House and Senate have approved a bill in identical form, the bill is sent to the President. If the president approves of the legislation, it is signed and becomes a law. If president opposes the bill, they may veto the bill. and it will be sent back to congress.
If the president vetoes a bill, congress may attempt to override the veto. If both the senate and the house pass the bill by two-thirds majority, the Presidents veto is overruled, and the bill becomes a law.