begin with the end in mind
Too often, a portrait is simply a picture of a smiling face. Pleasant enough to look at, but unfocused in its intention and therefore less likely to properly fulfill any given purpose. Ideally, a portrait should be made with the end purpose in mind. The visual language of an image will vary depending on the intended use. For what, exactly, do you need images? One purpose? Several? This informs and directs the process. Whether you want something for professional applications, online dating, social media, or to commemorate a special time, how you'll use the images and how you want to be perceived in them will shape the images that are made.
A smarter process for superior images
I believe that maintaining a smarter process yields better results. In practical terms, this primarily means spending a little time before the photo shoot to really clarify what you want as a final product. This may sound obvious, but you'd be surprised how rarely it is done with any real depth. As previously mentioned, the final application of the images will determine a lot. But there are other factors to consider, too. For example, how do you want to be perceived in the images? Confident? Kind? Funny? Intelligent? What are the things you want to avoid in your pictures? What do you like or dislike about existing pictures of you? What are examples of portraits of other people that you especially like or dislike?
By coming to a clear understanding before the camera even comes out of the bag, the whole process gets easier for everyone involved. It becomes easier for you to relax in front of the camera, which makes it easier for me to get good images. If we know more clearly what it is we're trying to achieve, the whole process can be made more efficient. It also just plain helps ensure that the overall quality of the images is high.
If it sounds like a lot of work, don't worry. My method may require a little bit more effort from you than simply sitting and smiling while I point a camera at your face, but anything worth doing well is going to require at least a little work, and subjects often find the experience enjoyable. When you're more involved in the process, you also feel a greater sense of satisfaction with the final result, which is good for everyone.