Start with the big global changes then progress to local edits.
My basic workflow is as follows:
1. Set the white point with the Exposure slider (or use the white point slider in Levels).
2. Use Recovery to pull back some clipped highlights if there is undesired clipping. Don't worry about specular highlights like reflections off water.
3. Set the black point with the slider (I prefer to have a small amount of clipping on the darkest areas, but this is very image dependent). You can use the black point slider in Levels as well. Some images don't need to have a true black, don't feel obliged to add black areas to a high key image for example. Misty images also may not have a black and if you force one you will lose much of the mist effect.
4. For overall brightness - use the Brightness slider, or pull up or down on the middle of the Curves, or move the middle slider in Levels.
Look at the image and see if it looks fine, and sometimes it does. If it doesn't you have to decide what else it needs.
5. More contrast - use the contrast slider (or do an S curve with Curves)
6. More local contrast - use the Definition slider (touch up recovery if needed). I almost always add a bit of Definition.
If some areas are too light or too dark.
7. Curves - click on the icon that allows direct selection of a tone in your image (in the curves box) then click on a problematic area of your image. This puts a point on your curve that you pull up or down on to lighten or darken respectively. Repeat for multiple areas if needed.
8. You can also use the Shadows and Highlights sliders to tweak the darks and lights.
You may find that the global adjustments are fixing one area, but wrecking another.
9. Pick the control that fixes the issue, then hit brushes and paint it in, or paint it out of the area you don't want altered. Do whatever is easier.
10. You can go farther and spend a lot of time do local dodging and burning to get the tonalities exactly as you want them.
11. I almost always Vignette (usually 0.3/0.3 or 0.4/0.4) to get a gentle darkening of the corners and edges.
Colour
12. White Balance the image (I actually do this at the beginning before any other edits). You may want to make your image neutral, or warm or cool to taste depending on the subject and mood. Generally I click on something grey to get a neutral WB and sometimes I will warm it up a bit with the Blue / Yellow slider.
12. Play with Saturation and Vibrance, and even the Colour panel if you want to target a selective colour. These can be brushed in or out if you don't want global changes. I often put Vibrance at 10-20 and Saturation at 5-10, but this is very taste and image specific.
There are many ways to do the same thing. You just need to figure out what tools you prefer and use them. From a speed perspective avoiding local brushed in edits is quicker, but for your favourite pictures it is worth taking some extra time to get everything perfect.
Have fun,
Richard