I encountered this little basket in a couple of children's origami books, so it should be easy for adults and children alike.
Start with a square piece of paper and fold it in half from corner to corner. If you are using origami paper, the color on the inside of these first few folds will end up on the outside of the basket. (The paper below is dark pink and pale pink and the basket will end up being light pink).
Unfold, and then fold again from the other corner to the other corner and unfold again. You are doing this to create creases.
Now fold from side to side in both directions and unfold again. Your square piece of paper will now have creases crisscrossing it from corner to corner and side to side.
This next part is tricky so I've provided a few photos. Fold it back in half again from side to side, grasp the two sides in your hands, and sort of squeeze them together so that it all comes together as shown below.
You'll end up with this square.
Put it down on the table with the open edges and corner at the top, make it nice and flat, and then take the top corner of the top layer and fold it down towards the bottom corner.
Press down on the crease.
Next, as though you were turning the pages of a book, take the right corner of the top layer and bring it over to meet the left corner.
Repeat the steps you just did above - take the top corner of the upper layer and fold it down to the bottom corner again, and then "turn the page" - take the right corner of the upper layer and fold it over to the left.
Smooth out the paper and press down on creases after each step. The folds you just did should now be on the inside. Both sides of your square should look like the photo below.
Now, take the right corner of your top layer and fold it about two-thirds of the way towards the left.
Repeat this step for the left hand side, overlapping the two sides, and then tape down to secure.
Turn over and repeat again on the back side - fold each side in towards the other so they overlap and then tape in place.
It's best to use the smallest piece of tape you can.
Next fold the bottom corner up and press on it to make a crease, then let go.
Now, gently grasp the basket on both sides and open it up. The last crease you just made helps form the bottom of the basket.
Use your fingers as needed to help sharpen the creases and give the basket some shape, especially around the bottom and the sides. Tape the bottom in place.
Now take the two handles and secure them together at the top with a little bit of tape.
You're done! Use a craft punch and contrasting paper to decorate as you like, or leave it as is. Little ones love these baskets for carrying tiny toys, acorns, pebbles, and other treasures.