Painting a portrait with a likeness to the subject is a challenging task--even for most professional two-dimensional artists. Only time and practice can really improve your results. Remember that the first portraits you paint likely will not look very much like your subject. Keep trying.
Draw several preliminary studies of your subject in a similar pose to the pose you will be painting. These studies should be relatively quick but not sloppy. Familiarise yourself with the features of your subject.
Draw an image of your subject on the canvas or paper where you will be painting. Do not worry about details---draw the larger shapes and contours only. Note if you are painting in water colour, draw very lightly. Watercolour is a transparent medium and your lines may show up in the final product.
Lay down flat expanses of colour with a relatively wide brush. Do not address details at this time. For example, cover the face in flesh tones but do not add the colour of the cheeks or shadows around the eyes or nose. This will be added in later.
Step back from the painting and compare the subject to the painting. Look for any obvious mistakes or distortions. Repeat this step as necessary (generally after every step) throughout the rest of the painting process.
Paint larger details, using a smaller brush than you used in step 3. For example, paint the irises and pupils, paint the eyebrows, and shadows defining the ridges of the nose.
Paint the finest details, such as a few clumps of individual hairs and eyelashes. Use the smallest brush possible.
Flick your eyes back and forth quickly between the subject and the painting. Try to look at the painting and the subject both as nothing more than a series of shapes. You may wish to blur your vision slightly when doing this, to disassociate the image of the person with your preconceived notions of what that person looks like. Make adjustments as necessary.
Show your painting to someone else. Ask for suggestions and constructive criticism.
If you still feel like something is wrong, try turning the painting upside down for a fresh perspective. When you come to step 8 (asking for suggestions), remember not to get defensive. Be open minded, and thank your critic when you are done. It helps to ask someone who is an artist. If you still are not satisfied with the likeness of the painting to the subject, try stepping away from the portrait for a week or two, and return when you feel like you have forgotten what it looks like.