Qamar Ul Islam: How to Develop Your Photography Skills:

Learn the basics, if you haven't already. Basics of photography include composition, which is essentially the placing of a subject within the frame of a photograph, lighting, and the basic workings of your camera. See How to Take Better Photographs for some introductory material.
Be ready. At least half of the time, the difference between a great photograph and a mediocre one is being in the right place at the right time, with a camera in your hand. Carry your camera with you as often as you can. Make sure to use your camera often, too. Just carrying it around does no good.
Be there. Being "ready" is not enough. As Ken Rockwell says of his early experience,

Did you catch the spoiler word in my logic, "anything that presented itself?" I was a spectator. I thought that photography involved taking pictures of things that came along. NO! You have to get out there and find things. Finding and seeing are the hard part...[t]aking a picture of what you find is the trivial part.

So get up, get out there and take photographs. Go out at every time of day, every day, and look for things. Don't wait for the right opportunity to come along (but be prepared if it does!); go out and find them. Look for opportunities everywhere you go (whether you're at the mall or on the other side of the world), and go to places to look for opportunities. If you can see something in your mind, chances are you can set it up and shoot it!

Stop looking for subjects to photograph and learn to see.

Look for colours. Or do the opposite: look for a total absence of colour, or shoot in black-and-white.

Look for repetition and rhythm. Or do the opposite, and look for something completely isolated from the things around it.

Look for lighting, and the lack of such. Take photographs of shadows, or of reflections, or of light streaming through something, or of things in total darkness.

Look for emotion and gesture if you're photographing people. Do they show happiness? Mischievousness? Sadness? Do they look thoughtful? Or do they just look like another person mildly annoyed to have a camera pointed at them?

Look for texture, forms, and patterns. Great black-and-white photographs are stunning because black-and-white forces the photographer to look for these things.

Look for contrasts. Look for something that stands out from the rest of the shot. In your composition, use the wide end of your zoom (or a wide-angle lens) and get closer and make it so. Look for contrasts of all the things above: colour amid dullness, light among darkness, and so on. If you're photographing people, try putting (or finding) your subject in a context in which they stand out. Look for happiness in unexpected places. Look for a person in a surrounding in which they appear out-of-place. Or ignore this and take them completely away from their context by opening your lens all the way to blur the background. In short...

Look for anything that will hold a viewer's interest which isn't a traditional "subject". As you find your niche, you'll probably find that you end up going back to taking photographs of subjects again. This is fine. Looking for things which aren't subjects will improve your photography no end—you'll soon see a different world altogether.

Keep your photos as simple as possible. Get as close to your subject as you can. Use your feet, and use your zoom lens (if you have one) to fine-tune your composition. Get rid of anything that doesn't give some important context to understand your photo fully.

Shoot film. If you already shoot film, then shoot digital as well. Both film and digital cameras have their place in the learning photographer's arsenal. They both have their advantages and disadvantages, and both will teach you a different set of habits. The worst habits of digital, are balanced out by the better habits of film, and vice versa.

Digital cameras give you immediate feedback on what you are doing right and what you are doing wrong. They also reduce the cost of experimentation to zero. Both of these things are invaluable to the new photographer. However, the zero cost of digital makes it far too easy to fall into the habit of "spraying-and-praying" and hoping a good photo comes out at the end of it.

Film cameras force you to be more careful about what you are taking. Even a millionaire would be reluctant to sit around on his yacht taking thirty-six photographs of his bathing towel on film.^[1] The economic incentive to make more of the shots you take might lead to less experimentation (which is bad), but it does make you think harder before taking photographs (which can be good, if you have a good idea of what you should do before taking the picture). What's more, film still has a look all its own, and you can pick up professional-quality film gear ludicrously cheap as well.

Show the best of your work to other people. Which is to say, find the best of your work and show only that to other people. Even the greatest photographers don't take superb shots every single time; they're just very selective about what they show to others.

Be brutal about it. If they're not great shots to you, then never show them. Your standards will increase over time, and even the ones you might have once thought were passable will probably look pretty lame to you a few months down the line. If this means that all you had for a day's worth of shooting was one or two photos, then that's okay. In fact, it probably means you're being just harsh enough.

Don't look at images full size. Ken points out that the most important parts of an image are those that can be seen when the picture is seen at thumbnail size. There are people out there who will pick at flaws they can only see in 100% crops of your photos. That's okay, because they aren't really worth listening to. Feel free to pass over anything that doesn't look great when it takes up a quarter of your screen (or less).

Seek out and listen to the critiques of others. Don't fall into the trap of posting in "critique my photos"-type threads on the Internet; these are usually full of the pixel-peepers mentioned above. Still, it's good to seek out constructive criticism, as long as you're careful about who you listen to.

Listen to artists. If someone has some great artistic work to show— photos, paintings, music or anything else—then this is reason to take them seriously, since other artists instinctively understand visceral impact, whether it's in their field or not (and if your photo doesn't make an impact, it's probably better deleted). Most non-artists do, as well, although they aren't as well positioned to tell you what you're doing right (and they're more likely to be nice to you to avoid hurting your feelings).

Ignore anyone who critiques your photos harshly and has no stunning photography to show. Their opinions are simply not worth listening to.

Figure out what you're doing right and what you're doing wrong. If someone liked a photograph, what made them like it? If they didn't, what did you do wrong? As said above, other artists will probably be able to tell you these things.

Don't be modest if someone likes your work. It's okay, photographers love beingcomplimented on their masterpieces as much as anyone else does. Try not to be cocky, though.
9 Look for work that inspires you. This doesn't mean merely technically impeccable; any (very rich) clown can stick a 400mm f/2.8 lens onto a $3000 digital SLR, get a well-exposed, super-sharp photograph of a bird, and that still won't make them Steve Cirone. Rather, look for work that makes you smile, laugh, cry, or feel anything, and not work that makes you think "well exposed and focused". If you're into people photos, look at the work of Steve McCurry (photographer of the Afghan Girl), or the studio work of Annie Leibowitz.

If you're on Flickr or any other photo-sharing website, then keep an eye on the people who inspire you (though don't end up spending so much time at your computer that you're not out taking photos).

Learn some technical trivia. No, this is not the most important part about taking photographs. In fact, it's one of the least important, which is why it's all the way down here; a great photo taken by a point-and-shooter ignorant of these things, is far more interesting than a boring photo perfectly focused and exposed. It's also infinitely better than the one that wasn't taken at all because someone was too busy worrying about this sort of trivia.

Still, it's handy to have a working knowledge of shutter speed, aperture, focal length, etc., and what effects they will have on your picture. None of this will make a bad photo into a good one, but it can sometimes keep you from losing a good photo to a technical problem and can make great photos even better.

Find your niche. You may find that you're a good enough communicator to photograph people. You may find that you enjoy being out in all weathers enough that you can do landscape photography. You might have huge telephoto lenses and enjoy motor racing enough that you find yourself having fun photographing them. Try all these things! Find something that you enjoy, and that you're good at, but don't limit yourself to it.

Tips

Don't get discouraged. If your photos still aren't showing any progress after a few days or weeks, keep at it! Photography is also about patience and dedication!
Buy a modern book on photography. Save money and buy a used book as long as it is relatively current. Sample and look at many photography books before buying. Also, look at a variety of magazines (music, people, homes, gardens, architecture, babies - whatever interests you). How do the pictures look? What are the photographers doing?
Print your best images in a reasonably large format.
Give yourself a tutorial. If you own a camera and have its manual, read the manual and play with the options as you read. Read in a place where you will not be distracted.
Automation exists for a reason: it allows you to concentrate on getting great photos rather than on technical trivia you shouldn't have to care about. Use your camera's "Program" mode, if it has one, and use the program shift to select different combinations of apertures and shutter speeds. If you can only get good results in "Manual", use it, but pretending you're in the 1950s and lacking any kind of automation doesn't make you "pro".
Make a concentrated effort to make every shot count. Typically, one shot in twenty might be a keeper, one in one hundred is good, one in a thousand is a "Wow" photo, and if you are lucky, you might get the shot of a lifetime over your life that everyone can appreciate.

Maybe your dad or a photographer friend has a redundant film SLR kicking around?

Don't have a camera? Borrow one until you can buy one. Having your own camera will be an immense help.

Many of the photos in this article were taken with completely obsolete cameras. Do you care?

Nearly any digital camera from the last decade, and nearly any film camera ever made, will be good enough to get you great shots. Don't worry about gear until you've got the basics down. Even better, don't worry about gear, ever.