Here's something to get you started.
First click on 'B&W":
That will change your image to black an white and open up the 'Black and Whiet Mix' panel:
The little symbol that the arrow points to lets you make adjustments to how the colours from the original image map to gray levels in your black and white image. Click on that symbol. That changes your cursor to a + sign with a circle and arrows thingy.
Now you take your cursor to the image and choose a part that you want to have a different grey value. Click there and drag up to make all the parts of the image that share that colour lighter. Drag down to make them darker. Repeat for other parts of the image that were originally other colours. It's easy and fun. Go try it.
I dunno how far you wanna go, but the Google/Nik plugins have a great B&W plugin called Silver Efex. There's also Tonality by Macphun if you're on a Mac. Or custom presets by other authors, like http://www.lonelyspeck.com/film-speck-one-102-free-lightroom-presets/
Here is an example of what using different HSL Presets will do for a natural photo to convert it to B&W, where the top right Desaturated is what things look like if you just turn down the Saturation slider as far as it'll go, whereas the High-Contrast Red & Blue are LR Presets and you can see how the change the emphasis on the flower vs the background:
Here is another fun treatment of a natural subject using alternating values of the HSL sliders to create dark and light rings:
Perhaps more importantly is the Split Toning area at the lower-right, where instead of having things shades of pure gray, I made the dark colors a little bluish-green and the light colors a little reddish-brown to give a pseudo-aged look. The Split-Toning Balance is used to determine how much is greenish and how much is brownish depending on how light or dark the overall image is.
Here is a good example of what can be done with the HSL sliders. These are original orange mushrooms with yellow cracks across the top on green grass. I manipulated the sliders to separate the orange and yellow on opposite ends of black and white and also made the green grass white, so only the shape of the mushrooms is dark. If I merely desaturated the image the orange of the mushroom and green of the grass would have been a similar gray tone.