Well it's pretty easy, just follow these steps to make a poster in the style of a Soviet Propaganda Lithograph.
First maybe you should look at some real examples: Soviet Propaganda Research
Step 1: Create a New Document
Open Photoshop and create a new document with the settings 8x10 inches @ 72dpi.
Step 2: Wrinkled paper
I changed the color and brightness of this image a couple of times over the following steps until I got something which went with my color scheme; I added a 'color mask' with which I set to Multiply at 55% transparency and I adjusted the images hue and saturation a bit.
Step 3: Imagery
Step 4: Desaturate
If you want to keep some of the original colors go to Image > Adjustments > Hue/Saturation and reduce the saturation to a desired level.
Step 5: A poster aesthetic...
I used Poster Edges for my first image.
Step 6: The time is now
Double click on the layers for your image and wrinkled paper and do the following steps:
select color overlay - choose the color you wish
change the Blend Mode to Multiply
then change the Opacity to about between 50 and 75%.