Step 1: Material
Avoid contruction paper or any paper with similar consistancies; they do not end up in clean finished prouducts. Computer paper works fine if you cannot find anything else. (Actually, normal comuter/ printer paper is ideal for most origami projects, its just not colorful. It gives nIce clean folds and is fairly cheap as well as easily accessible.)
Step 2: Creasing
Basically you need to make a 6x6 square using creases. There are two ways to do this. You can either fold the paper in thirds, and then each one of those thirds in half, or you could fold the whole paper into an 8x8 square and cut of two rows or squares from two of the sides (No picture). If you are a beginner, I highly recommend you try the second method, folding thirds can be a pain with unpracticed hands.
Like the famous saying goes, a picture is worth a thousand words. Refer to the pictures for a better understanding
Step 3: Creasing Continued
Then take the bottom edge of the paper and fold it up to the closest one sixth crease.
Once again, refer to the pictures.
Step 4: Mountain Folding
Step 5: Squash Fold
But if you don't completely understand, you basically create the triangles by grabbing the corners and fold them to the center line. You then unfold, grab only the top layer of the paper, and fold it up to the upper crease. You then flatten it. You should end up with a dimond shaped fold. Repeat on all four sides.
Step 6: Flip, Fold, and Tuck
Step 7: Finishing
Step 8: Poof! Its There!
Enjoy your vase. :)