How many sides does a regular polygon have if one exterior angle is 90 degrees? 3 4 5 6?

The easiest way to do this is to find out the interior angle and divide that number into 360. (The figure is regular meaning all sides are equal. And so are all interior angles).

The interior angle is always the supplement of the exterior angle. In this case 180 - 90 = 90 which is the interior angle.  The regular figure you have drawn is a square. It has 4 sides.