Fold in half to make a rectangle with your desired side facing out (for us it's the patterned side as shown). Then pull the corner to the mid crease, bisecting the corner shown in the upper right. Unfold and repeat with the upper left corner, then unfold.
Completely unfold the paper and repeat the above on the other side, starting with the upper right corner. Unfold and check that your creases match the photo, then spin your paper 180 degrees so the top edge is now at the bottom edge.
Swing the right "wing" to the left, hinging at the center line. Bring the point of this wing down to meet the bottom center point and crease your fold. Repeat with the other wing.
Then create a valley fold in each of the "inner triangles," bringing the creased edges you just made to the center line and flatten the form as shown.
Use this new crease to invert the center bottom corner of the flap and re-flatten, as shown.
Repeat on the other side.
Fold each front leg in half lengthwise to give them shape.
Turn your attention to the broad back end of the frog. See those bits of paper showing out from under the cape? Fold them to the interior of the frog to hide them.
Fold each leg over to make the hip. The exact angle isn't important, just keep the legs consistent.
Fold each leg back onto itself and create another crease parallel to the hip.
You can stop here for a perfectly respectable frog! If you want to create extra bounce and a more 3D form, unfold the bottom half of the frog and then fold the whole frog in half at its center back. Bend the "belly" to one side to create an inversion that helps tuck the frog's rear under itself while doming the back.
To carry a battery on board, simply sandwich the LED leads around the battery (flip it around until it lights up) and tape the assembly inside the frog. Adjust the angle of the LED to suit your taste.