Processing digital images to simulate film is a *huge* topic on photography websites. If you ignore all the discussions and products sold to do this, and just look for Photoshop tutorials by Googling {film look photoshop tutorial} or {film simulation photoshop tutorial}, you get about 2,000,000 hits for each search.
If, instead, you search for film simulation plugins or actions, ie, {film look photoshop plugin} or {film look photoshop actions}, you get about a half-million hits for each of these searches. Most of the major plugin packages (eg, Nik Color Efx Pro, the suite of Topaz products, etc.), popular on-line efx (eg, Instagram), and even point-and-shoot cameras usually come with some built-in film effects.
In addition to the current popularity of retro / nostalgic "film looks" (especially among schmaltzy wedding photographers), another reason for all this interest is that there are an infinite number of starting points, and a huge number of "film looks" due to the different types of film and processing combinations over the past 100 or so years, so it's hard to generate truly authentic effects, but everyone keeps trying.
Since you want to get into this, probably the best way is to train your eye to see all the different classic types of flaws exhibited by film. For example, as Clare pointed out in reference to the image you posted, film exhibits every type of color "error" one can imagine, eg, blacks and whites that have color casts (usually different), curve crossings (different gammas for R, G, and B), hue and saturation shifts (both when fresh, but especially after film ages a few years).
As I pointed out in reference to your posted example image, another typical film flaw is
halation and the less well-known corresponding spreading of dark areas.
Another big class of film "errors" that are commonly simulated to give a film "look" are inaccuracies in the brightness of different areas. Slide film had easy to burn out highlights, whereas negative film shows big tonality problems in dark areas where the negative is thin. The example image you posted shows both of these problems.
The final big class of film "errors" that I'll mention is film grain. It's not the same as digital noise, and it's probably the most common effect offered by the film-look plugin / action cottage industry. Fortunately, at the resolution we are viewing your example image, film grain doesn't seem to be a big factor.
I'll also point out that in addition to film problems, lenses from 50-100 years ago introduced their share of softness and other aberrations that become a bit part of the overall look of photos from that era.
So, for you, with all of these possibilities, the question is where should you start.
I REALLY liked the suggestion by Spruce for you to try Picmonkey.com. For example, I feel that this
before-and-after Picmonkey pair exhibits some of the more important features I see in your example image (ie, softness, blow and spreading highlights, muddy and spreading blacks, color shifts). Picmonkey's on-line effects service lets you play with (ie, learn / train your eye) many of the above effects with a very easy-to-use user interface, albeit with some really odd, non-technical names.
Each one of Picmonkey's effects typically require several Photoshop low-level adjustments to replicate, so immediately trying to do these things in PS without becoming familiar with all of the possibilities in a general way is most likely to be overwhelming and not the best way to become proficient in this area of post processing. Then, once you have the general lay of the land and know what film features are important to you, you can come back and ask more specific questions like,
"What's the best way to simulate xxx using PS's native tools?", where xxx could be
"film grain",
"halation",
"muddy blacks",
"off color whites",
"lens softness", etc.
Sorry this was so long winded, but there is a lot to the question you asked.
HTH,
Tom M
