Step 1:
This vase is folded out of two square papers glued together. Glue or tape three papers together if you want a wider vase.
Valley-fold over this line.

Step 8:
The arrows show two places where the layers are folded together.

Step 6:
Repeat step 5 over these lines.

Step 12:
Make sharper folding lines.
Use tape or glue to keep the bottom closed (if necessary)

Step 11:
Make the same mountain-fold at the bottom of the edge, which is not visible in this picture.
Now you can place the edge on the right over this edge, see pink arrow.
Glue or tape both edges together.

Step 10:
The large arrow shows the corner of step 9.
Repeat step 9 on the other three corners, see smaller arrows.

Step 9:
Fold/push this corner downwards.

Step 5:
Make an inside reverse fold over these four sets of three green lines.
Valley-fold over the four orange lines while you do this.

Step 7:
Press the layers between the two large arrows against each other, then fold them together over the short green line.
Do the same on the other 7 same places, see smaller arrows.

Step 3:
Fold in half over this line,
then unfold the model.

Step 2:
Fold in half over this line.

Step 4:
Prefold over these three lines.

Step 13:
The bottom of the vase should look like this.

This video by Joost Langeveld also has instructions for the Origami vase (Joost is a popular You Tube artist):