The only way to improve your picture taking is to take picture after picture after picture.
Firstly, you need to take photographs and often. I find it beneficial to find a focus – a theme – and to take as many of those sorts of pictures as you can. For example, if you want to practice natural light portraits, then there is your theme. Other themes could be landscapes, photojournalism, events, architecture, night time, and more.
Secondly, and often missed by amateurs: don’t shoot your subject just once. Shoot your subject a dozen times. Then you will cull the best photograph or photographs from the shots you took. You may find some have flaws you didn’t see before, or you may have several “good” shots with one fantastic shot.
Don’t limit yourself. If using film, shoot an entire roll on an event – or more. If using digital, get the biggest memory card you can get and shoot as much as necessary.
Lastly – once you are done get comments on your photographs. Photo clubs are good for this, as is Flickr Groups for photographers.
A photo a day makes a good project as well – and you can post it to Flickr as well.
Remember – have fun!