First of all you`ll have to know what are curves and what they do. It is a tool that helps you improve the luminosity/darkness of some specific targets (Shadows , Midtones , Highlights ). You can easily increase the brightness of the dark areas so some details return to the photo.
This tool can be used in two modes. The first one is to go from the top menu to Image – Adjustments – Curves or by pressing CTRL + M. This method is preferred if your changes are correct at any time and you don’t want to remove them later. The second mode is to press the forth button from the bottom of the layer window. This method will make a new Adjustment Layer which you can hide later if you don`t like the result.
Take a photo , open it and use the second method. A new box will show up.
You can use this tool in two ways. One of them let you modify the curve using points that can modify the curve so it fits your requests. The other one lets you draw the curve using the pencil from the left panel. I insist using the first method because it is easy to use and you can correct more accurate the settings. If you feel confident enough about your skills you could use the pencil to draw the curve but this could be time consuming and you don`t always achieve the desired effect.
There are 16 squares. You can divide them in 3 major sections. The four of them from the top right , the four of them from the bottom left and the point that intersects in the middle. If you drag the top part of the line up you will increase the brightness of the Highlights. If you move it downwards you will darken the highlights. The same thing applies to the bottom part of the line , but you change the Shadows settings. If you want to work with the Midtones you have to drag the middle of the line (at the intersection of the 2 large squares).
The good thing about this tool is hat you can easily increase the contrast by making an S-shape line.
You can also set the channels individually , but this is more advanced and you will have to practice some time on the RGB to see how things work.
This tool also has three eyedroppers. You will mainly use the middle one. Look at the photo for a Neutral Gray spot (this spot should contain a gray like the one of the box , so the tool can adjust the White balance properly) and with the eyedropper click on it. It will adjust the white balance correctly if you found the right tone. If not , CTRL+Z and try again.
This is one of the most useful tools if you learn how to use it correctly. Photographers use it a lot to adjust the White balance of photos and to get rid of some color if you work on individual channels.