

Select the image carefully
Let's take this picture as an example and create the same effect in Photoshop.
Add contrast and saturation
Place the image in a separate layer. Click the adjustment layers menu icon in the Layers palette and choose "Brightness/Contrast". Check the preview option. Set the Contrast to +20. Hit OK. Click the adjustment layers menu icon again and choose "Hue/Saturation". Set the Saturation to +20. Click OK.

Adjust the curves

Add one more adjustment layer. This time choose "Curves.". Choose the Red channel and make sure the edit point icon is selected. Change the curve line a bit as show above.

From the Channel dropdown menu, pick Green and adjust the curve as shown above.

Choose Blue from the Channel dropdown menu and adjust the curve as shown above.
Add Vignette effect

Chose the layer with the photo and navigate to Filter > "Convert for Smart Filters". By doing this you can apply filters to the photo while keeping the original intact. You'll get a message that says the layer will be converted into a smart object. Click OK. Now you'll be able to adjust the filters you've applied at any time.

Now navigate to Filter > Distort > Lens Correction. In the Vignette option set the amount to -100 and the midpoint to +50. Click OK. The Smart Filter will appear below the layer. Double click on it and this will open the Lens Correction filter options again. Double clicking the slider icon on the right will give you the option to adjust the layer mode and the transparency of the effect on the layer. Set the value to 70%.
Add some Colourisation

In the Layers palette click the adjustment layers menu icon again and choose "Hue/Saturation". Check the Colorize option in the bottom right corner as well as Preview. Drag the sliders until you get a sepia duo tone effect as shown above. Change the opacity of this adjustment layer to 50%.
The final touch
A small thing should be done to give the photo a real vintage touch. Click the adjustment layers menu icon in the Layers palette again and choose "Solid Colour". Select a very bright hot pink magenta colour and click OK. Change the opacity of the layer to 5%.

Before and after

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