All three branches of government have the ability to make laws.
The Congressional branch can make laws through legislation.
A member of either the House or Senate may introduce a bill and it must be approved by both. If similar but different bills are passed by the House and Senate, a conference committee will attempt to reconcile the differences and then both will vote on the same thing. Before it can be a law it must also be approved by the President or, if he does not sign the bill, the House and Senate can vote on it again and if they both pass it by a 2/3 majority it becomes law.
The Executive branch can make laws as when the president issues executive orders.
Executive orders don't carry as much weight as congressional laws but they mean a lot more when Congress passes an executive order.
The Judicial Branch can make laws through the precedent of Marbury vs. Madison. The precedent allowed the court systems the power to declare acts of the state, legislative, and executive branches of the federal government null and void if they violate the Constitution. Two different thought ways of thinking about the courts making laws.
Judicial Activism- Belief the courts should actively use their own judgement to interpret or create laws to correct wrongs that have not be corrected in the system on issues such as civil rights, individual rights, etc.
Examples: Roe v Wade (abortion), Brown v Board of Education of Topeka (civil rights), Planned Parenthood v Casey (contraceptive rights), etc.
Judicial Restraint- Belief the courts should interpret the laws as they are exactly written and not engage in policy making. Often they will say that it is a political question to be resolved by the President or Congress.
Examples: Luther v. Borden (legitimacy of local government), Bush v. Gore (election dispute), District of Columbia v. Heller (gun rights), etc.