You can learn to design printables with free options like Canva, or Paint. These programs are fine for basic designs, but can be very limiting. If you would like completely custom designs, programs like Adobe Photoshop and Illustrator are excellent.
You'll need adhesives to assemble certain printables, like attaching cupcake toppers to paper straws. A printable designer's go-to adhesive is usually a hot glue gun. They're inexpensive, and the glue is guaranteed to keep everything in place. You can also use glue dots, double sided tape (permanent is preferred), glue sticks, or regular tape.