Step 1:
This bag is folded out of polka dots wrapping paper taped to shiny purple wrapping paper, cut/folded into a4-size.
Prefold in half over this line

Step 8:
Press these two edges inwards with your finger by making an inside reverse fold over the yellow lines.

Step 6:
Pull the edges of the rectangular part upwards. Then valley-fold over the two yellow lines.

Step 13:
Press the bag inwards from aside by folding over these three lines. Do the same on the other side.

Step 12:
Valley-fold over this line. Then tape or glue the edges of the bag together.

Step 11:
Make an inside reverse fold over these two sets of three lines.

Step 10:
Prefold over these two lines. The part between both lines is half the width of the bag itself.

Step 9:
Prefold the pink part in half.

Step 5:
Push/pull both corners to the right by making an inside reverse fold over the yellow lines.
Valley-fold over the pink line while you do this.

Step 7:
Valley-fold over these two lines, the flaps go under the rectangular part.
Then, press everything flat.

Step 3:
Valley-fold over these two lines.

Step 2:
Fold the edges to the centerline

Step 4:
Valley-fold over this line.

Step 14:
This is how to close the bag.

Done!

This video by Joost Langeveld also has instructions for folding the gift bag: