With a little practice, post processing can make a poor photo reasonable, but it's best to start with a good photo. So get reading up on photography basics. You don't need a fancy camera to learn how to compose a good photo.
Take a little look at this guide on the Rule of Thirds (how and where to put things in the photo)
http://www.golfgtiforum.co.uk/index.php?topic=114170.0Here's my edits of one of the best from that bunch:
Colour:

Black and White:

That was done with an ancient version of Photoshop 6 cos I'm at work and don't have access to the much better/latest Photoshop CS5.
What makes that shot interesting is the depth looking through the walls to the next wall and the next wall beyond that. It has interest that is central to the photo and draws your eye in.
That camera is quite old now, I remember using a friends one about 9yrs ago, but it does have some manual modes, so you could get instructions out and learn how to use all the options on it. Learning how to get a faster shutter speed (for moving things/kids/pets/cars) or how to get a higher ISO (make the sensor more sensitive to light for low light/interior photos).
I would also turn off the digital zoom. The 6x optical zoom on that camera should be more than enough and once you start using digital zoom, you lose quality.
You can definately get some good photos from that camera, just learn how to make the most of it. See here on flickr for some examples using that camera:
http://www.flickr.com/search/?q=fuji%20finepix%20s602This one is also interesting, the sky is blue, the grass is green but look at the building, it needs a bit more space around it to show context, where is it, what's around?

Here's an old example of my old car, up on a huge hill and you can tell. The car itself is not that interesting, but the location makes it interesting.

A few other tips,
1) don't point the camera to the sky as you'll just end up with an overexposed sky (ie it goes white)
2) in bright sunlight you probably don't need to bother using the tripod (it's anchoring you to the ground, get moving about):
3) put the camera to your eye and move yourself, turn, crouch, move sideways, climb something to change your view and see if it looks more interesting.
4) look at what is in the middle of the photo, this is what the camera will focus on and the rest may end up being out of focus, is that what you want ?
5) Since its digital, take a couple of photos from slightly different angles and see which one works.
Experiment, enjoy.