For this example we'll convert this photograph:
A quick way to see the individual channels is to use the channels palette. Click on a channel to see that channel in grayscale.
Here is an animated GIF that cycles through all three channels (click on the image to enlarge. The channel name is in the bottom right corner). You'll notice that the red channel has the best shadows but it also has the most noise, especially in the top right corner. The green channel has less noise but also has lighter shadows.
Select the RGB channel to revert back to it's original color. Then go back to the Layers palette and create a new Channel Mixer layer. For this example I'll set the channels to 50% red, 40% green, and 10% blue.
Notice how changing the sliders also changes the overall brightness of the photograph.
Here's the result:
You'll want to set the channel values so that it totals to 100%. This will maintain the overall brightness of the picture. However, you can also use the Constant slider to adjust the overall brightness.
You can set the channel sliders between -200% and +200%. See Channel Mixer Theory to see how this is applied.