I've wanted to do this ever since I can remember: write a series of blog posts about photography. Not just about my photos, but about how to improve yours. I'm finally making a start. Here's the first in the series, about possibly my favourite form of photography: portraits.
1. Simple backgrounds work best.
When shooting portraits, more often than not, you will want your subject to be the main focus of the shot. If the background has more points of interest than the subject themself, the viewer's attention will naturally be drawn to the surroundings. This may be what you're trying to achieve, to show the subject's environment perhaps, but if otherwise, clear the background as much as possible. If your bedroom is cluttered, move somewhere with not as many extraneous items or pieces of furniture.
With portraits, I recommend using a plain, single-coloured background. Avoid pastel tones (unless you are shooting in black and white) as they will "wash out" the subject (this is why I almost never shoot portraits in colour at home). Instead, opt for a vibrant hue, or better, black. You can purchase large sheets of coloured cardboard at craft and [some] discount stores, or you can just use some coloured fabric – even a doormat works!
2. Use the rule of thirds.
Have a look at the guide here if you're unsure. However, it can be just as effective to break the rule of thirds and place the subject right in the centre...
3. Fill the frame with the subject.
That's right: do a close-up. To be honest, I really don't understand what so many people have against close-ups: is it because they're insecure; have they had bad experiences in the past; have they never seen good close-ups before? I'm personally a huge fan of them because they focus less on materialism (what you're wearing and holding doesn't matter) and more on emotion.
There are two ways of achieving this: physically moving closer (which does not always work, especially with those with "personal space" issues), and zooming in.
Many people make the mistake of including too much headspace. Note this well: space between the subject's head and the edge of the frame is almost never necessary (unless you're planning to do an image cut-out). Instead, try starting at the hairline, or even just above the eyebrows – in this way, using the rule of thirds, the eyes should naturally be placed along the points of intersection.
Also, a proper portrait should never, under any circumstances, have other random people in the background!!!

4. Use the light source; don't turn your back to it!
Another extremely common mistake is having your subject face away from the sun or light source. If the sun is behind, the background will be well-lit but your subject won't. The result is that your subject will appear as a silhouette, and their features will very likely be difficult to make out. Photoshop can fix this to an extent, but your subject will become very grainy if you try to brighten an underexposed image/section.
If possible (and do realise that it is at times impossible), have your subject facing the sun so that the source of lights hits the front of them instead of the back.
However, just like breaking the rule of thirds, it can at times be just as effective to use the silhouette effect...

5. Use the macro setting.
When taking portraits, it may seem obvious that you should shoot in portrait mode – and you should, if you want to keep the subject in focus and blur the background – but I actually prefer to switch to macro mode, which most compact cameras have these days. (Look for the flower symbol.) Using macro, you can focus on particular points of interest, while blurring out the rest of the frame's contents. In this way, you can draw attention to the little details. I personally like to focus on eyes.
6. Keep your arms out of it!
This one's just for self-portraits (euphemism for "camwhoring"). You know, those shots where you're holding the camera out in front of you at arm's length? Ok, so you may think your arms are really attractive and all, but let's be honest here: they really aren't. They just aren't professional either. Especially if you're female and your arms are quite the opposite of hairless, in which case all of that hair will be magnified by about 24x. Not a pleasant look.
The easy way to solve this? Zoom in. In most cases, that's all you need to do.
7. Go semi-candid.
Posed shots can be good. That is, if your subject isn't the type who does a reaaaally fake, cheesy smile in front of the camera, or who stiffens up when they see you with a camera in hand. Candid shots, on the other hand, are often more natural, but they can sometimes end up being outright embarrassing for the subject.
So what can you do if neither of them will work? Simple: go half-posed, half-candid. Let your subject pose for a photo, press the shutter button, and tell them it's done. Take the real shot when they think it's over and loosen up. That's your opportunity to get some genuine smiles, and perhaps even capture laughter on camera. Pure, unadulterated joy.

B&W or colour?
Colours are nice. Or at least they are when your colours are vibrant – pastel colours, as I've said, will simply wash out the subject. It really comes down to personal preference when choosing which mode to shoot in, but even colour-enthusiasts have to admit: colours can be distracting.
In portraits, more likely than not, you will be aiming to capture the emotion of the subject, and colours tend to bring the viewer's attention elsewhere – to the vibrancy of the hues, for example. On the other hand, by shooting in black-and-white, the viewer will immediately be drawn to what matters most: the features of the subject. Their emotion.
However, very few compact digital cameras work well in B&W mode, producing dull and rather boring shots. I recommend first shooting in colour, and then converting the photos to B&W when you get back to your computer. It makes a significant difference in terms of the intensity of the tones.
That's it for now.
Hopefully, using these tips will improve your portrait photography – but remember that sometimes, rules are made to be broken. Simply following every rule out there will not guarantee that your shots will come out well – just choose the ones you believe in and use them. Most importantly, have fun taking photos and experiment, experiment, experiment!
Next in the series: The megapixel war: do they actually matter?