I figured out how to make this once whilst messing around during a chemistry lecture. That would have been around 1995. I do not even know if there is a "proper" way to make an origami penguin, but this one seems to work fairly well.
I've just done some simple sketches and scanned them in. Hopefully you'll be able to figure them out.
It starts off in a similar fashion as making a frog. The main difference at this point is that we also folder the paper length-wise before hand.
At the end of this step you should have a piece of paper with 3 "valley" folds, which intersect each other.
Next we make another fold, but this one is a "mountain" fold. It should intersect the other 3 folds and should run the width of the paper. It must also be at 90° to the length-wise fold. Then pull in the folds to make a triangle (as in step 3 of making a frog).
Next we will make what will become the penguins head and beak. Simply fold the top of the triangle down until it touches the bottom of the triangle (not the bottom of the paper, but the bottom of the actual triangle). You can then pull this back up once the fold has been made and turn the penguin over.
The next bit is quite tricky, but just sit and think about what you are trying to do. You want to get the folds that are in the third drawing above. i.e. two folds that start where that "head fold" and the "length-wise fold" intersect, run parallel to the slopes of the triangle and finish at the edges. You must also make sure that these folds do not intrude into the "head" of the penguin.
To do this take one side of the penguin and fold it back (making a "valley" fold), so that one side of the "head fold" goes through 90° and touches the "length-wise fold". Crease the fold then repeat with the other-side.
Next fold the head forward slightly and pull the sides together along the length-wise fold. You should get something like the middle picture, with the "head" up at an angle to the "body" and two trapezium shapes sticking out to either side.
Then push the head forward and pull the trapezium shapes into the body (you will need to crease the folds to make everything stay flat).
At this point you should have something that looks like the first picture shown above. It looks sort of penguin like, but a bit fat! Just fold some of the "body" inwards so you get something like the second picture.
Now simple pull out the triangles on the side to makes wings (these were the ront legs when were making a frog) and pull the body slightly apart so the penguin can stand.