I should make a standard posting about this ...
1. For portraits of a single person, use aperture priority (A or Av on your mode dial) and a low aperture, thus blurring the background so the viewer will focus on your subject. Inform yourself about the lens you're using. Some are kind of soft when completely open (i.e. at highest aperture, or lowest f-number), so step them down a bit if you want sharpness (but some softness might even be good for portaits). Others are fine even wide open. For example I can use f/1.8 on my 35mm f/1.8 DX prime quite nicely, its just a bit soft at the borders, but the center is already very sharp.
Ideally you want a lens thats sharp and has good Bokeh, i.e. good behavior in the out of focus areas of your picture.
2. Since this starts to appear quite often in pictures: set your camera to ISO 100 (or whatever ISO your camera works best at, again inform yourself about that, some cameras actually work best at ISO 400 etc). If you get above maxium shutter speed with this, you might want to try grayfilters to compensate.
3. Always set the focus on the eyes.
4. Always try to get some nice light to the eyes, not too much, to add the extra magic everyone wants in a portrait. But dont make your subject squint or worse, get watery eyes.
5. Good focal lenghts for portrait are between about 35mm and 135mm, relative to full frame (for example my camera is APS-C / crop factor 1.5, that means my 35mm lens is 53mm relative to full frame). Where 35mm is really only full body standing, and 135mm is face only. A good compromise is 85mm which still allows full body, but also smaller framing, as long as you have enough room.
6. The ideal distance between person portrayed and camera is about 5 meter. More far away means people will start to look somewhat flat. Closer means people will be increasingly distorted.
7. Harsh sunlight, as it is typical for a beach without clouds, are the worst light you can possibly have for a portrait. It will cause hard shadows. If you have to photograph in harsh sunlight, the typical strategy is to put the person between the sun and the camera. This way the person portrait will not squint from the sunlight, and the sun will create a nice outline of the body. You can then use fill flash and/or reflectors (artifical or natural ones, like white house walls or large white rocks) to put some more pleasing light onto the front of the subject. Avoid light that comes from too much below, it will make look people kind of freaky, an effect popular in movies for monster characters like Dracula.
8. Shadow is much better, but again you want some light into the eyes of your subject, with the same tricks as before.
9. Cloudy is also much better, making people having almost no shadows at all, with the sky working as a huge "softbox" that diffuses light into all directions. But its can also be somewhat undramatic.
10. The "golden hour", i.e. the minutes of dawn and right after sunrise and right before sunset, is the best light for portraits (and landscapes), since then there will be the most interesting light. While the name is "golden hour", the actual time might be much slower (or somewhat longer).
11. If you have a cheap camera that doesnt support high sync speed mode, i.e. cannot use a flash at shutter speeds above x-sync, but you still want to use fill flash, you may want to get a couple graycards so you can lower your shutter speed to whatever flash sync speed your camera has (for example, my camera has 1/200s as sync speed. More expensive cameras might have 1/250s or even better).
12. Another idea is to have a moveable flash, i.e. a flash with which you can flash from the side.