Depending on how long the toilet seat has been in place, the fasteners may be coated in debris. They come off much more easily once the debris is removed.
There are two different designs for toilet seats: one with a permanent stud mounted on a hinge and another with a stud that is removable from the hinge. If the stud can be removed, a mechanism on top of the hinge can be rotated to separate the two pieces. Both designs employ a plastic nut that has to be rotated counterclockwise to remove the assembly.
Most toilet seats currently employ a quick-release design for ease of installation. To reassemble, insert the plastic bolt into the hole and thread the plastic nut clockwise from underneath the toilet bowl. Once both studs are installed, press the hinge on and rotate the mechanism to lock the hinge into place.