To simply darken the edges of the frame equally and smoothly, you would use the vignette adjustments;
Classic Vignette Photo Effect - Photoshop Tutorial
I am not a photoshop user but there is more going on in those images than adding a vignette. To achieve the effect of a halo surrounding the subject as seen in a few of the images you are going to need to apply brushes and localized masks.
With these tools you can apply subtle (or not so subtle) contrast, luminance and sharpening adjustments to specific areas of the image;
vinetting photoshop - Google Search
vinetting photoshop - Google Search
Keep in mind and even research the connections between, say, sharpening and adding contrast and boosting luminance. Many of the adjustments you will perform in post production will be subtly adjusting similar values. Keep the histogram for each image in your screen and when making adjustments also watch the histogram display to assure you are not over adjusting any one value which will cause blown out highlights or overly darkened shadows. Research photoshop curves;
photoshop curves - Google Search
You can also add degrees of "creative blur" which will make your subject standout from the backgrounds;
photoshop tutorials blur - Google Search
One of the best techniques for learning the how and what's and why's of photography is to learn how to backward engineer an existing image you admire. The same advice applies equally to the processing of an image (with certain restrictions when looking at the work of a paid professional with several layers of discrete, individual processors being applied).
Learn the basics of the tools available to you in your version of photoshop and then backwards guess at how the image was created using those tools. Try them out on your own images and see how well you've done at guessing how an image was created from start to finish.
I would suggest you use a search engine to find your version of photoshop. Then find a general guide tutorial to its available effects/tools. Not every version will have very feature so its somewhat important you work only on the version you have available for use.
The images in that collection though have been fairly heavily edited IMO. Not always very subtly either. Skin tone adjustments are a different matter all together.
You might begin with a general tutorial on portrait processing;
photoshop tutorial portraiture - Google Search
Though, whether you are trying to make corrections, adjust skin tone or simply brighten a face are all somewhat unique tools and effects;
vinetting photoshop - Google Search
You can safely bet the images you show have been processed from a RAW data file.
That means they will probably not be available for use if you are shooting/working with a compressed Jpeg file.
Finally, I wouldn't want to try to capture exactly what another photographer has done and is showing in their portfolio. Chances are they may have gone through several different processors to achieve their final image. If you don't have all of the software they have used, you will not get what they turn out.
Every photoshop effect has a tutorial you can access.
Every photoshop effect you view on line has a image catalog attached to it which can help you narrow down which tools to use for a specific effect.
View the images in the catalog and get a sense of what you want to achieve - other than a bit by it recreation of someone else's work - and try them out. As long as you have a back file for the original image, you have nothing to lose and everything to gain through experimentation.
Additionally, workflow is somewhat important to the final look of an image. Not everyone works in the same way with similar images. Adding sharpening at this stage vs that stage can effect the look of the image. Take a look at how various photographers work on portraits;
photoshop prtraiture workflow - Google Search
If you're in a time crunch and need to replicate an effect quickly without understanding what you are doing or how you are doing it, I suspect a photoshop pro will add more specific instructions in another post.