Here is a simple exercise you can do anywhere that will help develop your photographic eye. Take your camera with just one lens and go for a walk (of course any point and shoot camera will do the trick too).
While walking down the street, at the park or even in the wilderness, make a point to stop randomly and find something to photograph within 10 or 15 feet (3 to 5 m) from where you are standing.
Better yet, if you are walking with a non photographer, ask him or her to tell you when to stop. Look up and down, look all around you and take your time to find something interesting to photograph. It can be a scene in the street happening just in front of you, an architectural detail, the manhole cover on which you are standing or an insect on a flower.
If you are using a DSLR limit yourself to one lens but experiment with a different lens each time to make the exercise more interesting. The point is to learn to make the ordinary look extraordinary. Try different angles, a shallow depth of field, etc. Or try some magic in the digital darkroom later!
Another idea is to get children involved in this exercise. A perfect way to get them to walk and introduce them to photography at the same time. Their discoveries might surprise you! This exercise can also be helpful if you are planning to start a 365 day project.
Here are a few examples of pictures taken during this simple exercise. I like details, in architecture or in nature and I also like to shoot with a very shallow depth of field. The goal of this exercise is not to produce fine art photographs. Consider it as a photo assignment with no pressure and see what happens.
The possibilities are endless, just remember to have fun