For instructions on how to make the modules and put them together, see my Modular Origami How-to here:
Each row has 17 modules. So in total, you'll need 172 modules:
39 for the tummy (white)
131 for the base (pink)
2 for the flippers (pink)
The tummy, starting from the top, has:
Everything else will be your base color (pink, in my case)
You will probably need to stick your finger into the holes in the top and bottom in order to make your penguin more round. As such, do not glue on the face, flippers, or hat until you're sure the penguin looks the way you want it to look.
The eyes are made by hole punching two holes and coloring them black with sharpie. The beak and bowtie were cut free hand.
The hat was made by first cutting out a circle, then cutting a "pie slice" out of it and gluing one side down to make a cone. Then I wrapped a strip of paper around this and glued it onto the penguin, making sure to cover the hole at the top of its head.
I used a dab of glue to keep the flippers in place, but they should stay reasonably well on their own if you'd like to forsake the glue and keep it "real" origami.