Whether designing your own cover or covers for other people, there are plenty of guidelines as to how to design to genre, etc. (Techniques and tutorials are listed under our Cover Design category, coming soon.)
A graphics program is non-negotiable.
As with interior formatting, Adobe is the gold standard. Several Adobe products may be used for cover design: InDesign, Photoshop, and Illustrator all come into play, depending on genre, type of print media, etc. They’re available by subscription.
Please note this is not a comprehensive list, but cites the most widely-used programs for book cover design and illustration.