There are a lot of ways to convert an image into black and white. You can use Lightroom, Photoshop or Tonality Pro from Macpun.
But now the Nik collection is available for free and I had great fun trying out the Silver Efex Pro.
I started out in Lightroom and followed my normal workflow to edit the picture. Then I transferred to Silver Efex Pro. Photo > Edit in > Silver Efex pro
Under the copy file options, there are some important fields:
On the right side you can tune the image exactly the way you like it
You can do this globally but also locally using the control points:
With Compare you get to see the difference between the edited version and the original.
So when you're done, save the image and it will be reimported into Lightroom. If so needed, it's here you can do more editing.
Check out this video if you want to find out more.