Choose your image carefully
First of all I need to mention that some pictures are better suitable than others. It's a good thing to experiment a lot and find out if the result is to your liking. Btw, not all settings I suggest are written in stone. Sometimes you discover the best effect by accident. How it looks good for you also boils down to personal preference. Let's take this picture as an example and create this same effect.
Add contrast and saturation
Place the image in a separate layer. In the Layers palette click the adjustment layers menu icon and select "Brightness/Contrast". Check the preview option so you see the direct result. Set the Contrast to +20. Hit OK. Click the adjustment layers menu icon again and select "Hue/Saturation". Set the Saturation to +20. Hit OK.
Add another adjustement layer. This time choose "Curves...". Select the Red channel and make sure the edit points icon is selected. Change the curve line a bit as show in the image above.
Select Green from the Channel dropdown menu and adjust the curve as shown in the image above.
Now select Blue from the Channel dropdown menu and adjust the curve as shown in the image above.
Add Vignette effect
Select the layer with your photo and go to the Filter menu and select "Convert for Smart Filters". Doing this means you can apply filters to the photo while leaving your original in tact. First you'll get a message that says the layer will be converted into a smart object. Click OK. With this approach you'll be able to adjust the filters you've applied at any time. These Smart Filters work a bit like Adjustments layers but then with filter effects.
Now go to the Filter menu and select Distort > Lens Correction. In the Vignette option set the amount to -100 and the midpoint to +50. Hit the OK button. You'll see the Smart Filter appear below the layer. Double clicking this will open the Lens Correction filter options again where you can adjust anything you want. 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%. Now that's pretty neat stuff if you ask me :)
Add some Colorisation
Your photo should look pretty dramatic right now with a lot of contrast. Now we'll tone it all down again, but of course with a special effect to make it look like an old photo. In the Layers palette click the adjustment layers menu icon again and select "Hue/Saturation". Check the Colorize option in the bottom right corner as well as Preview. Drag the sliders until you get a bit of a sepia duo tone effect on your photo just as shown in the picture above. Change the opacity of this adjustement layer to 50%.
The final touch
You could say OK we're done, but there is one little accent that our photo needs to give that real vintage touch. These photos always have some pinkish glow as if colors are faded from the sun. Therefor click the adjustment layers menu icon in the Layers palette again and select "Solid Color". Select a very bright hot pink magenta color and click OK. Change the opacity of the layer to 5%. That's it. Now you should have a vintage photo.
Before and after
Here is another example:
Make sure you experiment with the settings of these adjustement layers and filters. Like I said before the outcome differs a lot on the chosen image and also on the settings. My apologies to Marco that it took some time to bring this online. Hope you enjoyed this tutorial and learned a few things again :)