Frame and panel doors are typically joined using groove and tongue or mortise and tenon joints.
Another simple but effective option is the mitered door, where the rails and style are equal in width and joined at the corners by biscuits or other suitable reinforcement.
The key to these types of doors is to ensure that the 45 degree mitered corners are perfectly cut and aligned before glue up. See how this challenge can be easily overcome by using a simple jig you can build yourself.