Making an origami puffer fish is quite a task to wrap your mind around. Your average person wouldn't know where to start or how in the world you can make this oddball aquatic organism out of only a square sheet of paper. Fortunately the idea is not only possible, but the process of making it is not as complicated as you'd think. You'll start with some standard square origami paper, make a unique series of folds, and there you have it. You're labour over a hot sheet of paper will be well worth the spectacular origami puffer fish you'll be adding to your 100 per cent recyclable origami aquarium.
Place your square sheet of origami paper in front of you so that a side and not a corner is pointed at you. Fold your the origami paper in half towards the side that is away from you. Unfold it, turn it 90 degrees, and fold it in half again. Unfold it, flip it over in the direction away from you, and turn it slightly clockwise so that the paper is now like a diamond with one corner pointing at you.
Fold the corner closest to you toward the opposite corner. Unfold it, turn it clockwise 90 degrees and fold the corner that is now closest to you toward the opposite corner. Unfold it. You should have what resembles a three dimensional four point star due to all the folds. Fold all the inward folds representing the sides of that star inward toward the centre creating what looks like a simple origami tent from the side. Flatten two adjacent sides of the four against one another and do the same for the last two sides resulting in what looks like the triangular tip of a directional arrow.
Fold the right hand corner of the superficial portion of the triangle toward the centre of the triangle (there's technically a second triangle and corner beneath the top or superficial one). Unfold the previous fold. Fold the same part of the triangle toward the top corner of the newest fold or crease that was just created when folding that same corner towards the centre of the triangle. Unfold this fold halfway, then open up the sides of this fold forming a pocket. Take the corner of the triangle you've been working with and fold it toward the other corner of the pocket resulting in a small square. Using the same corner as before, fold the bottom left corner of this newly formed square toward the top right corner of this very same square.
Fold the right side of the superficial "triangle" with the new square-like addition over to the left corner of the superficial triangle. Fold this same side of the superficial triangle that you just folded over in half so that the bottom of it now aligns with the centre of the triangle and the square is visible.
Fold the edge with the square down and to the left so that a certain crease you already made which heads straight along the bottom of the square is now aligned with the fold you had just made in the previous fold. One corner of the now flipped over and no longer visible square should be touching or slightly hanging over the edge of the bottom of the triangle towards the left side. Fold a small portion of the top left corner at the middle of the upper left side of the triangle (from the same superficial flap you've been working on) over so that the edge of this funkier fold is headed inward compared to the parallel side of the flap.
Fold the flap of the superficial triangle you've been working on back over to its original side revealing what now looks like a puffer fish eyes. Repeat the previous folds on the opposite side that is positioned against the already formed fin. Once completed, fold the upper non-eye side toward the top of the triangle so that the bottom aligns with the side (use the superficial or upper, visible side first). Fold this fold in half so that the upper corner now touches the centre point of the bottom. Fold the side corner of the flap that now looks like half of a diamond toward the centre crease. Unfold this crease halfway and open up the flap slightly forming a subtle opening. Take the most superficial corner of the flap at the bottom centre of the triangle, and fold it in half over what looks like a 45 degree slant taking advantage of this small temporary space (pocket) then pressing the pocket formed by unfolding halfway the previous fold back down. This complex fold forms what looks like a small knife blade pointed at a downward slant and crossing over the triangle's centre crease.
Fold the "knife blade" back at the part where the "blade" meets what was the edge of the temporary pocket used to create it (up at a slant towards the side of the triangle). This forms the rest of the fish's body including the puffer fish fins. Repeat the previous folds to form the opposite side of the front of the puffer fish's body.
Take the flat-on-its-side fish and spread open the top flaps and bottom flaps a little (tops include square-like eyes while bottoms include regular side fins). Adjust the eyes so that they're not flat against the side of the fish by tilting the whole squares along the centre fold they rest on toward the centre of the puffer fish.
Don't give up after the exhausting first round for making the eye part and the fin part. The second round (on the opposite side) goes much smoother and quicker each time.