There are various ways of making a Photograph Black and White in applications like Adobe Photoshop or Adobe Photoshop Elements. But it becomes important to know right workflow which can give good results with least efforts. The choice of workflow becomes important when we want to leave some part of the photograph in colors. Let's see how to achieve above shown results in Adobe Photoshop Elements...
Let's go step by step and I assume that you will be trying this in parallel -
1. Open your Photograph in Editor workspace of Adobe Photoshop Elements. Go to File Menu and opt for Open option.
2. Now select Smart Brush on left side Tool-Bar. The one highlighted in below image is the one which activate Smart Brush.
3. Now you will see a drop-down on top (just below Menu-bar). Expand the options and select 'Black and White' Category.
4. There are various types of Black & White preset available. You have to experiments and choose the one which is more suitable to your style of photographs. I am choosing 'Cold Tone B&W'
5. Not start selecting the area which you want to convert into Black & White. As you start moving your brush, that particular region will start changing into Black & White.
Try this technique and feel free to comment back for your further questions around the same.