Step 1:
I taped a newspaper page to a white paper of about 30x40 centimeters. Valley-fold over these three lines, start with the upper line.

Step 8:
Prefold the white edge over these lines.
Then push the edges between the arrows against each other, see next picture.

Step 6:
Unfold the fold of step 3.

Step 13:
Make sharper folding lines here.

Step 12:
Make sharper folding lines on the four edges between the arrows. Tape or glue them together, if necessary.

Step 11:
Tape or glue both ends together, see arrow.

Step 10:
Repeat step 9 three more times, see arrows

Step 9:
Press the edge indicated by the arrow over the edge on the left of it.

Step 5:
Prefold the edges to the centerline

Step 7:
Prefold over these lines. The line on the right is a normal fold, so no prefolding.

Step 3:
Valley-fold over this line.

Step 2:
Prefold over this line.

Step 4:
Prefold in half over this line

Step 14:
Use tape or glue to make a stronger bottom, if necessary.

This is a DIY video for making the newspaper Origami vase: