How would you go about making this photograph the way it is with Photoshop?

Depends what the original photo looked like. Without a reference to the original photo, I’d guess that it has been colorized, the contrast has likely been adjusted, it was either sharpened or a filter has been applied, possibly a colored overlay since it is so highly saturated in some areas.
Then plain white text in what looks to be Times New Roman, it doesn’t appear to have any special effects.

I’ve had a go at replicating the effect and here’s how I did it.

Start with a black and white/greyscale photo.
Add a background layer underneath the photo and fill with solid colour (in this case a slightly desaturated red).
Your b&w photo is now the top layer. Change the Layer Mode from Normal to Screen.

You may wish to play around with Brightness and Contrast (brightness down, contrast up) depending on the original photo.

Done.

A light red layer set to screen.

The album cover is from 1987 if that helps anyone determine the technique.

I know you asked about Photoshop, but…I was able to get a very similar effect using Picasa’s (free) duo-tone effect (orange/white).

In 1987 that would have been done merely by just printing a black & white photo with red ink.

@dabbler Here is a Google of certain amount of images by Morrissey for The Smiths records

So pretty much they were all printed in the way you describe? Do you happen to know the technique called? Or a link to the method? Analogue rocks!

I think that would be plain old photo-lithography.

Thin aluminium sheets with a photo-sensitive ink-resist layer are exposed like a photo print to light from the negative. The resist layer is rinsed away where not exposed. The part without resist can pick up ink, the plate is inked and used to print the album covers.

Newspapers and magazines are printed using this method. Where there is color photography the printing is typically done with four separate printing steps, cyan, magenta, yellow, black.