how do i lighten or darken selected areas of a black and white photo

Michael, I don't mean to diminish the value of Dodge and Burn tools, but they do have a notable shortcoming; each dodge or burn dab is incorporated into the images. This makes it impractical or impossible to undo one or more of the changes minutes later, when other dabs have been added elsewhere in the image. Instead, you must then pile correction on correction rather than undoing or modifying the original image values.

There is another option – one that puts the dodge and burn adjustments on a separate layer where they may be seen at any time and each adjusted or even eliminated, returning the area to its original value – all without corrupting the original image. The following instructions take longer to describe than to do.

1. Add a blank layer and then choose Edit > Fill and from the double-arrow options of the Use field, choose 50% gray. Then click OK. The image area will become gray overall. Next, change the Blending mode in the Layers panel from Normal to Overlay. The Background image will return although you will be working on Layer 1.

2. Do not use the Dodge and Burn tools. Choose the Brush tool and adjust its size, hardness and opacity. Dab or stroke with the Black to slowly add density. To lighten an area, dab or stroke with White. Although the image will reflect the changes, they are being recorded on Layer1 and may be viewed by turning off the eye in the Background layer. Best of all: to undo any tone adjustment and return the area to its original value at any time, simply return that area to 50% by cloning from an adjacent unretouched area in Layer 1.

This can really depend on your level of expertise.  Probably the easiest is using the Dodge and Burn Tools (attached image).  However, as your skills advance, I'd suggest using Levels and Curves along with layer masks.

I would start by copying the image layer with Ctrl/Cmd+J. 

Apply one or more Adjustment Layers -- Brightness/Contrast, Levels, Curves or Exposure.  If you don't like the results, you can discard the adjustment layer and start over.

You will find dodge and burn tools in the tool bar. I recommend creating a new layer and apply those tools on the new layer. This allows you to have more control.