To begin, feel free to download the image provided for an easy follow along.  It's a simple beach scene that could use some touching up, but it makes for a good photo that has different values in it.  First step is to duplicate the background layer.  Drag it down to the page looking icon "duplicate" layer, or simply right click on it and hit "duplicate layer". Next, hit the half circle icon at the bottom of your Layers palatte (known as the "Create new fill or Adjustment layer" icon) and select the "Channel Mixer..." option from the list.
The Channel mixer dialog box will now open up, and you will see a few options.  Under the Source Channels, you'll see options for your Red, Green and Blue, but first below that, at the very bottom left, click the "Monochrome" box and make sure it is checked.

Next, go to the Red, Green and blue settings and adjust to something similar as what I have in the image here -->.
You want percent values that all add up to 100%.  For instance, I use a simple method of starting with 40 for the red, 60 for the green, and 0 percent for blue.  Adjust and play around and see what works best with your image at hand.  Be careful when working in the Blue channel, for it can give you harsh effects.

When you have completed and hit the "ok" button in the Channel Mixer dialog box, you should have something similar to the image here on the right in your Layers pallette.  That completes the steps, but there's something very important about what you've done here.  First, rather than the more common way of going to Image>Mode>Grayscale (destructive), you've set up a non destructive adjustment layer above your original color layer below.  You have many options now.  You can double click the half circle icon on the layer itself to re-open and make continued adjustments to that Channel Mixer layer.  You can also set the Opacity to a lower value and bring back in some more color, or all color.  The Channel Mixer adjustment layer even comes pre-set with a Layer Mask (white thumbnail box on the layer itself), which can be very helpful in specifing exactly where you want this layer to take effect in your image.  So you've set up an awsome grayscale psd file here with great versitility.  Make sure to save the file as psd when your done working on it, and you'll always be able to come back to it and re-adjust if you ever choose to do so.

That's it, enjoy!