To save money — to set aside money for the future or a specific goal (e.g., saving part of one's salary).
留学のために毎月少しずつ金を貯めている。
I am saving a little money each month for studying abroad.
車を買うために金を貯めた。
I saved money to buy a car.
老後のために金を貯める習慣が大切だ。
It's important to have the habit of saving money for retirement.