Assuming, then, that you're only using the aforementioned "good quality ingredients," here's how ice cream traditionally is made. After combining ingredients, the cold, liquid mixture (called the "base") is churned in a machine whose parts are icy cold. The "icy cold" part allows the creamy base to freeze from liquid to solid. The churning mixes air into it, increasing the volume, lightening the mouthfeel and softening the finished product, so you don't end up with an unscoopable — albeit tasty — giant white ice cube.
But here's how to make it without a fancy machine: