Genitals

Generally, you can differentiate both sexes in humans due to external sexual organs. In some birds, especially in penguins, it is not that easy. There is no dimorphism in penguin males and females. You cannot estimate the sex of a penguin by physical appearance definitely. In field studies researchers judge the sexes for example by measuring the bill lenght. In general, females have shorter bills than males but that is not always true. To be sure about the sex you have to observe a copulation (the male sits on top of the female) or make a DNA test.

Both sexes have a cloaca, this is a kind of collecting box where all excretions of the body are flowing into (products of digestion and gonads). Its opening is on the ventral side near the tip of the tail.
Males have no penis and the testis are displaced in the body. In females only one ovary and oviduct develops, mostly on the left side. This is the case in many birds because they have to reduce their weight for flying. This could be an evidence that penguins derive from flying birds.
During copulation both cloacas are pressed against each other. If the male ejaculates, the sperm will get into the cloaca of the female.

The pressure at defecation in Chinstrap and Adelie Penguins for watery material is about 10 kPa (77 mmHg) whereas material of higher viscosity is expelled with up to 60 kPa (450 mmHg). It is estimated that the pressure in humans is about 100 mmHg, so penguins can generate a four times higher pressure during defecation than humans.

References

Hocken, A. G. "Post-mortem examination of penguins." Wellington: Department of Conservation (2002).
Scolaro, José A., Martin A. Hall, and Isaías M. Ximénez. "The Magellanic Penguin (Spheniscus magellanicus): sexing adults by discriminant analysis of morphometric characters." The Auk (1983): 221-224.
Meyer-Rochow, Victor Benno, and Jozsef Gal. "Pressures produced when penguins pooh - calculations on avian defaecation." Polar Biology 27.1 (2003): 56-58.