Step 1:
This is an a4-size paper, it's wrapping paper cut into the right size.
Mountain-fold over these two lines.

Step 8:
Make an outside reverse fold on the left and right.

Step 6:
Make the same folds on the other side, use the prefolded line of step 5 as guidance.

DONE!

Step 12:
Glue both ends together, see arrow.

Step 11:
Valley-fold over these two lines.

Step 10:
Valley-fold over these two lines.

Step 9:
Glue these two parts together, see pink arrow.

Step 5:
Prefold in half over the short pink line in the middle.

Step 7:
Make an inside reverse fold on the left and right.

Step 3:
Fold in half over this line.

Step 2:
Fold in half over this line.

Step 4:
Fold in half one more time.
If your strip still isn't narrow enough you can just fold it in half until it has the right width.

Crafting with real paper clips is fun too, like making this bracelet for example.

Instructions for making the bracelet can be found here:   Dollar Store Crafts

You only need some bright colored paper clips to make it.

This paper clip is folded out of a narrow strip

Joost Langeveld is folding the heart shaped paper clip in this video: