With a little bit of care you can do some good work with the better quality 'point & shoot' cameras. I first went digital with a secondhand Canon Powershot G2. But be warned, when the nature photography bug bites you, it tends to get expensive later on.
Just experiment with camera settings. Try different shutter speeds and aperture settings until you get the hang of things. Nature photography is a bit more involved than snaps of friends, etc but it is basically the same. You need sufficient shutter speed to hold the camera steady and enough aperture to give sufficient depth to the subject. If you start to get serious think about a basic tripod.
For editing software. There are quite a few alternatives; Photoshop Elements is a popular starter, but I prefer Serif Photo Plus. But there are many other good choices ranging from freebies to around £50. You can easily spend around £1000 for top of the range software.
Basic starter editing consists of cropping closer to the subject and resizing; improving brightness and contrast; sharpening the image. There are many free internet photo tutorials to try, which will guide you from starter to advanced level. I particularly recommend
The Luminous Landscape and
Cambridge in Colour - Digital Photography Tutorials & Gallery but just look around to see what suits you. And then, come back here to ask more questions.