To draw Rei Ayanami, begin by sketching a large circle for the top half of her face, and add the lower half of the face. Notice that the distance from the top eye guideline to the bottom of the circle is about the same as the distance from the bottom of the circle to the chin; this should help you with the proportions a little. Draw the guidelines as shown. The eyes are not very large, so keep the guidelines for the eyes close together. The guidelines for the nose and mouth should be about the same distance apart as the guidelines for the eyes. Make sure you draw the guidelines lightly, because you are going to erase them later on.
Next, add the eyes, nose and mouth. The eyes should be spaced a little over one eye length apart. Notice that the bottoms of her eyes are not drawn in; they are defined by the irises, rather than lines. Rei isn't generally very emotive, so don't make the mouth or eyes too arched or exaggerated.
Next, erase the guidelines and draw in the basic outline of the hair. Rei's hair is very detailed, so for now, just worry about getting the shape of the hair to look right. Notice how the hair is separated into four main sections: the main part that comes down between the eyes, the two other parts to the left and right, and the round back part. Draw in the detail of her eyes, including the light glares and pupils. Although the bottoms of her eyes aren't drawn in, you can still tell where the bottom of the eyes are because of the irises. Draw her shoulders, as well. Rei has rather well defined shoulders (which is more apparent in the next picture), so don't just make them slope down like you normally would; you should be see the neck, back, and shoulder muscles, though they shouldn't be drawn as detailed and well developed as some of the Dragonball Z characters I featured earlier. ^_^ Just make sure you can see a little muscle definition.
Now comes the fun part: adding in all the detail. ^_~ The detail on the hair may look daunting at first, but just remember the basic shapes you drew in before, and add on to them. Add lots and lots of extra strands of hair, making them as thin and delicate as you can. Make sure you have some strands that come down over her cheeks. Draw her plug suit, making sure to keep the form streamlined, since it is a rather tight-fitting suit. ^_^ Again, make sure you show a little muscle definition around the shoulders. Try to make the oval things on her shoulders (I'm not quite sure what they're called) look like they are bulging out a little. Draw the things on her head, as well.
Color or shade your picture however you like. Make sure you use light blue to shade her plug suit, not grey. Her skin should be very pale, and her eyes should be red.
Next we'll try a 3/4 view. Begin by sketching a large circle for the top portion of her face, then add the lower half of the face. Her left cheek should bulge out slightly, and her chin should almost come to a point. Draw the guidelines as shown, making sure to keep the guidelines for the eyes close together, since her eyes are not very large.
Next, draw in the eyes, nose and mouth. The bottom part of her eyes should not be drawn in, since they will be defined by the irises. As always, she isn't particularly expressive, so don't exaggerate the features too much, and keep the eyes and mouth pretty level.
Next, erase the guidelines and draw the basic shape of her hair, leaving out the smaller details. Again, notice that her hair is composed of four main sections: the front main part that comes down between her eyes, the smaller part to the left and right of her eyes, and the larger back portion. Add detail to her eyes, and draw her eyebrows and neck.
Next, add the detail to her hair by drawing several thin, curved strands. Use the basic forms you drew in the last step to help you position them. Add extra detail to her eyes, like the eyelids and eyelashes. Draw the things on top of her head, and as much of her plug suit as you care to add. Erase all the lines you don't need, and clean up your sketch. I chose to ink mine before coloring it, because it makes the lines a lot cleaner and makes the picture easier to color.
Color your picture and add some shading, and you're done! :) Remember, just like before, she has pale skin and red eyes.