How can you make sure that an open cut does not become a scar?

You can't: Any cut leaves a scar. That is how we heal. How noticeable the scar is depends on the nature of the injury and how well one heals.

You can't : All cuts heal with scar tissue. What the scar ultimately looks like depends on the cut: how deep it was, where it is, the direction of the cut and how it was treated (if deep enough it needs suture). It also depends on the patient: skin color hereditary. Once it heals you can massage scar avoid sun. Topical silicone treatment may help.