Fish base
The fish base is a traditional starting shape made by folding a rabbit ear at two opposite corners of a square, giving a diamond with two long points and two small flaps.
Crease one diagonal. Fold a kite base toward that crease at one end, unfold, and repeat at the opposite end so both ends are marked. Then collapse each end as a rabbit ear: the edges fold to the diagonal together and the small flap that rises is laid down to one side. The two small flaps are often used for fins, legs or wings, and the long points for a head and tail.
Crooked flaps come from inaccurate kite creases, so make those precise before collapsing. Let each rabbit ear form on its own rather than forcing it, and point both flaps the same way. The fish base is named after the traditional fish folded from it; it also underlies many simple birds. None of the models on this site currently use it.