Assuming you are talking about a mayonnaise-based potato salad, it should be safe to eat for 3-4 days after it is made. Of course, this assumes you are storing it in the fridge. If you leave it out at room temperature, it will only be good for a couple of hours.
There are a few things you can do to help extend the shelf life of your potato salad. First, make sure the potatoes are fully cooked. Overcooked potatoes are actually lesslikely to turn brown and will hold up better in the salad. Second, add a bit of acidity. This can come in the form of vinegar, lemon juice, or even pickle juice. The acidity will help to preserve the potatoes and keep them from turning brown.
Finally, make sure the potato salad is properly covered. An airtight container will help to keep the salad from drying out and prevent it from absorbing any unpleasant odors from the fridge.