There is more to painting portraits than can be detailed here and there are plenty of helpful illustrated texts around to get you started, so I will summerize here the main points in constructing a portrait.
The main goal in portrait painting or drawing is to firstly obtain a likeness and secondly to convey the personality. Firstly though you are likely to feel pressured to get the likeness exact and in doing so will often make mistakes. The trick is to relax and enjoy what you're doing and observe the face as you would any object, involve yourself in angles and shape as you would a landscape and the likeness will come of itself. To get a likeness begin by looking at the overall bone structure of your sitter. Is their face thin or wide, oval or round? Is the jaw pointed or square? Is the forehead high or hidden by the hairline. These are the main benchmark features which will determine the all important outline of the face. Then begin focusing down on details within the face. Is the nose prominant or petite, what shape is it? Are the lips full or narrow? Does the age of the sitter show in wrinkles or in a youthful tightness? Do the eyelids droop? These are the elements held within the outline which must be considered. Focusing on finer detail still look at the shape of eyebrows and their relation to the eye, look at the cheeks and the hairline, look at the area under the chin and how the head sits on the neck. Are the eyes deepset, where do the corners of the mouth line up with the eyes? Do all this before putting pen to paper.
Most if not all texts demonstrating portrait drawing begin by drawing an outer oval for the size of the head and then dividing this egg shape with lines to space out eyes, nose and mouth. My personal technique departs from this norm, being self taught I have, in general, always begun with the line of the nose. My reasons for this are three fold. Firstly the nose is the only element to run vertically through the centre of the face with the elements of brows, eyes, mouth and chin placed at right angles, it is also easy to see the width and outline of the face using the nose as the reference point.
Secondly the nose shows the angle and direction of the head, again with all other elements at right angles around the curve of the face. Imagine the nose as a triangle. The tip of the nose points in the direction of the face, the line between filtrim and brow shows the angle of the head. Thirdly through years of practise I can also now determine the size of my portrait and even my figures by the size of the nose alone. Once I have established the nose I have the proportions for the rest of the head leading to the proportions for the body. Approx 8:1 for traditional figures.
Lighting of the face is most important. Because the depth of the face can be measured in centimetres we must ensure that the lighting will show all the necessary modelling of the features. Placing your lighting to one side and slightly high will give good shadows under the chin, lips, nose and eye. It will also cast one side of the face into more shadow with useful highlights on cheeks and brow ridges. I suggest looking at some good master portraits for ideas in lighting the face.
For instance notice in Léon Spilliaert's self portrait how he has used high contrast lighting to great effect and produced a portrait of great introspective intensity. Notice how the lighting is set high casting deep shadows under the brows and chin and how he has intensified this effect but using a white collar and negative white space to set the shadows against while the bright side of his face is completely surrounded in deep shadow.
Tip: Using high contrast to cast parts of the face into deep shadow you avoid problems of asymmetry as the eye will find its own line within the shadow.