Over time the materials and patterns have changed and many designs do not have the "iris eye" in the center or at all. I have done both and this card is done in the shape of a fan without an eye or a spiral.
On the inside I used a simple technique to make the frame for the verse. I cut the background rectangle first and then used a corner punch on all four corners. Then I cut the polka dot rectangle to fit inside dimensions and slipped it under the corner decorations which act as photo corners. Finally I glued the verse.
Iris folding is a lot of fun and lends itself to a wide variety of patterns and techniques. Patterned or plain paper can be used for the folded bits as well as material and foiled gift wrap. The strips are generally an inch wide and then folded in half so there is a clean leading edge. The back of the design is quite a jumbly mess but the outside is beautiful!
To help you get started I have found some tutorials...