These two settings usually go hand in hand, and therefore the Adobe Lightroom developer team have kept these two options together in the menu. They can be found in the collapsable 'Detail' section of the Develop module.
Sharpening help make our pictures look more crisp, the edges become more pronounced and the details can be enhanced.
Noise reduction is an essential setting which helps control the digital noise which is created by the capture of light by the cameras photosensor. The higher the ISO setting was when the picture was taken the more noise will be present on the picture. Noise exists as Luminance or Colour type.
As with all settings in lightroom the defaults can be reset by double clicking the text to the left of the setting. For example double clicking on Amount will reset the Amount of sharpening to the default value
The magnified view helps with making fine adjustments to our picture here. When adjusting sharpening amount try and find an area of the image with plenty of edge detail. Then gently move the slider back and forward to find the level suitable for your picture. Click on the magnified image will zoom in and zoom out.
The Radius setting is the size in pixels around the sharpening area that is effected by the amount of sharpening you applied. Changes here are subtle but increasing the radius above the default can cause a loss of detail. I rarely adjust this much at all and the default of 1.0 is fne for most.
Detail brings out edge details in the picture. This setting controls what gets sharpened in the image. Very fine detail will not necessarily get sharpened as much with a setting of 0, change this to 100 and watch even the very fine detail become more pronounced.
Masking - An often overlooked setting which helps temper the effects of the previous settings. Adjust this carefully and watch the noise dissapear. This tool does what noise reduction does for the overall image, but has specific effect on edge detail
On to the noise section.
Luminance noise is noticed most in areas of similar colour and tone, such as the sky. Zoom in on that part of the image and adjust the Luminance slider to the right to remove the noise in your picture. You'll want to move the slider back and forth until you find a level that is right for your image. As I mentioned earlier noise increases with the ISO setting your picture was taken at. If you took the picture at 100 ISO then noise probably won't be an issue. If it was night time and the lights were dim and you didn't use a flash then noise will be considerable if the ISO was 1600 or even 3200. You will want to shift the luminance slider up more in these cases. Too much noise reduction reduces the detail in your shots. Effectively it can remove sharpness and that is why we find sharpness and noise reduction settings together in the menu's. Noise reduction can also be used at more extreme levels to give the picture and almost watercolour look. Try this on portrait photo's to smooth out the results.
The detail slider underneath Luminance is used to control the loss of detail that noise reduction effects. The more you slide the detail slider to the right, the more it will control the luminance noise reduction. Try this when zoomed in for yourself. The contrast slider beneath the noise reduction can restore the loss of contrast that is caused by increased luminance noise reduction.
Colour noise is more apparent again on high ISO photos, especially those taken at night in dark surroundings. It is likely to show up as a fine dusting of speckles of colour on the photo especially around dark areas. Zoom in an adjust this slider to the right until you have reduced this to an acceptable level.