Modern cameras are getting much better at producing good photos, but older ones tend to yield pictures that lack in contrast and saturation and that aren't as sharp as they could be. And DSLRs used in the 'creative' modes, i.e. aperture priority mode, shutter priority mode, program mode, and full manual, tend not to process the picture too much as it's assumed that the user will want to take more control over the outcome.
I shoot RAW with my Nikon D1500 so I start off in Lightroom 3.6 by straightening and cropping, if necessary, then checking (and changing if necessary) the camera profile and white balance. Then I tweak the tonality using the Exposure, Recovery, Fill Light, and Blacks sliders plus the Tone Curve tool. I then bump the Clarity and Vibrance a little to bring it back to the way I saw the scene at the time I shot it; I might bump them a bit more if I like the effect.
Next I check the noise level and adjust it if necessary. Then I'll do any cleaning up using the Adjustment Brush, Spot Removal Tool, and Red Eye Correction tool. At this point I'll decide whether I want to get creative with this particular photo either in Lightroom by using the Tone Curve, HSL sliders, Split Toning, and the Grain and Vignetting tools, or in Photoshop Elements using selections, layers, masks, filters, and so on.
When I'm done with all that I'll sharpen the photo, either in Elements if I processed the photo that way, or in Lightroom. At this point, it's ready for export to Flickr, G+, or 500px.
I'd recommend that you check out the Elements tutorials on YouTube and consider joining the
Elements Village forum. Both will give you plenty of ideas. I second Nigel's suggestion of the Scott Kelby book and add a recommendation for Barbara Brundage's Missing Manual; Barbara hangs out at Elements Village and is a great help.
