Beate Johns has written a wonderful tutorial on how to make a criss-cross card. You can view it at:
http://www.splitcoaststampers.com/resources/crisscrosscard.php.
The instructions below create a similar card using less cardstock.
Supplies:
One 5 1/2" x 8 1/2" piece of cardstock for your card base
One 4" x 5 1/4" piece of double-sided print paper
One 3 3/4" x 5" piece of cardstock for insert
One 3 1/2" x 4 3/4" piece of neutral cardstock for insert
One 1 1/2" x 9" piece of colored cardstock for card band
Sticky Strip or Wonder Tape
Corner rounder
Ink, stamps, punches, embellishments
1. Score 5 1/2" x 8 1/2" cardstock at 4 1/4".
2. Take the scored piece and cut diagonally from center top to the bottom left corner.

3. Flip the triangle so the diagonal crosses the edge you just cut.
For a vertical card:

For a horizontal card:

4. Cut your double-sided print paper diagonally from corner to corner.
5. Adhere print paper triangles to your flaps.

6. Put Sticky Strip along the bottom and outside edge of your card base, and then adhere the loose triangle to form a pocket.
For vertical card:

For horizontal card:

7. Put Sticky Strip along the bottom and part-way up the edge of the remaining flap, and then adhere to bottom flap.
For vertical card:

For horizontal card:
Completed vertical pocket:

8. Take both pieces of the cardstock for the insert and use the corner rounder on the top corners.
9. Tape the insert layers together.
10. Wrap thin strip around card and adhere ends to form a band.
Stamp and embellish as desired.