There are lots of ways to do virtually everything in PS.
I don't use dodging and burning on an overlay layer too much because it isn't precise; it is difficult to use when I want to make specific uniform brightness changes to a specifically circumscribed area.
In a picture like this, the most important thing to do is to learn to see the defects in the image, diagnose what you think should be done, decide what needs to be brighter, darker, etc.
Since I want to darken the entire background, I select what I
don't want darkened, then copy and paste that selection. PS automatically makes a new layer with the pasted selection.(call that layer 1)
To darken the background, then I insert a levels or brightness adjustment layer just above the background and below the new layer 1.
Then I work on the figure, selecting the parts I want to darken, copying and pasting them on new layers with their own adjustment layers to darken or brighten them.
So what you have to know is:
- how to make and use layer masks (and channel masks)
- how to use the selection tools
- how to create and use layers
- how to create and use adjustment layers
- what are clipping masks and how to use them
This is clearly not something that can be covered in a thread but a week of work would get you some functional knowledge but not a ease of use or understanding what is best to use when.
I have been working hard at this for 4 or 5 years and think of myself as reasonably skilled for an amateur but
very far from expert. (Photoshop is the most complex program I have ever worked with and there are tools I still don't know how to use.)
It took me about 10 minutes on your image, working a bit quickly and a bit carelessly. To do this correctly it would take maybe 40 minutes because I'd be much more careful with masking and edges.
IMO, the totally best book to look most of this is
Photoshop Masking & Compositing (2nd Edition) (Voices That Matter): Katrin Eismann, Sean Duggan, James Porto: 9780321701008: Amazon.com: Books
This is worth every penny (although I like the older version better which is available used
9780735712799: Photoshop Masking & Compositing - New & Used Books & Textbooks at Alibris Marketplace )