Sketch with low strokes. Draw a human proportioned, oval-shaped, egg-like face. For easy shaping, draw a vertical and a horizontal line to make a cross, and draw the face around it so everything ends up in symmetry. Make sure the horizontal shaping line for marking the eyes is half way between the chin and the hairline. The line for the nose should be halfway between the chin and the eyes. Place a pencil mark halfway between the chin and the nose. This mark will be for the mouth.
Exaggerate by making a couple of changes in the rough face sketch you have drawn. Replace the curved chin with a sharpened, pointy one. While doing so, the jaw will automatically taper down from the eye level. Stretch down the eyes to bring them a little closer to the nose. For normal human drawing, the eye line is along the middle of the eyes but for an anime character, it may run along the upper half the eyes.
To make the eyes, place two lines on each eye to make upper and lower eyelashes and then draw a downward rectangle for the iris.
Start adding the details. Keep in mind that when it comes to anime drawing, you cannot add details as you would in a regular human sketch. Make simple changes, such as a tiny mark for a hint of nose. Similarly, make a mark only slightly bigger than that of the nose to specify the mouth. For the lower lip, just add a little shadow to the mark you placed for the mouth. Place two straight eyebrows just above the eyes, and make elongated, black pupils. Add a little shading to the iris. Add a highlight on the same side of both eyes, so the eyes appear to focus.
For hairdo, you get various options depending on your character's gender. No matter which hairstyle you draw, add pointy edges and sharp details rather than soft strokes. In fact, the hair should be the most exaggerated component. For instance, if you are drawing curled hair, it should be curled way up. Also, you cannot draw individual hair, rather the hair should be treated as a block or a volume that you can define with edges. To get some ideas on anime hairstyles, see the link in Resources below.
Clean up stray lines, particularly the grid lines you drew to shape the face. Also, draw the character's neck and make sure you keep it thin.