These are the before and after images:
1. Open your image.
2. Create a new layer. Layer > New > Layer. Set this layer mode to Screen.
3. Working with the new layer, Go to Edit > Fill. Use this setting:
Use: 50% Gray
Leave the Preserve Transparency box unchecked.
4. Now, go to Filter > Noise > Add Noise. Use this setting:
Amount: Just leave the default setting. Mine is 2.03%
Check the monochromatic option.
5. Next, go to Image > Adjustment > Auto Level.
6. Then, go to Filter > Blur > Motion Blur. Set the angle and distance to your preference. Mine is -76 for the angle and 56 pixels for the distance.
7. Now, we're going to adjust the density of the rain. Go to Image > Adjustment > Level. In the input level chart, slide the black and white slider until you get your desired density.
8. If the rain appear too sharp, go to Filter > Blur > Gaussian Blur. Adjust the radius to your liking. Not too high though. Mine is just 0.6 pixel.
9. One final step...Adjust the opacity of the rain layer until you get the perfect rain. And there you go, you've done your first rain effect in Photoshop.