Others have said most of it already, but here is my take.

The two main factors in an unsharp image are ISO speed, and camera shake. these factors work in opposition to each other.  The slowest shutter you can use without noticable shake will depend on how stesdy your hands are. With the camera set to shutter priority, try a few test shots  at diffrent shutter speeds in your back yard to finde your personal limit. Once you know your limit use the lowest ISO compatable with that shutter speed in any given circumstance.

A tripod can be cumbersome to lugg around all the time, a good compromise is a monopod with a quick release fitting. I always like to take one when I go out with my camera.

If you resize your photos on a PC the the very act of resizing will decrease the sharpness, even if you are reducing the size. As well as the sharpen filter, a clarify filter, or more contrast, can add to an impression of sharpness, even though the image is not actually any sharper.

Of course getting the focus right is another factor, sometimes auto focus can focus on the wrong thing, and you have to switch to manual.