Here is the photo that I want to make it look like it's raining.
I duplicated my original layer. Out of habit, I always do this to protect the original image.
Next, I created a new layer by holding down the alt/opt key and clicking on new layer.
This method opens up the options I want for my new layer.
I changed the blending mode to hard light and selected the "Hard light neutral color" box.
Next I added noise to this gray fill. Filter - Noise - Add Noise. Make sure to select Gaussian and the Monochromatic button. Adjust the noise to your liking.
To make the noise look like rain I went to Filter - Blur - Motion Blur. You'll want to add enough motion to add streaks but not long straight lines.
Because it appeared that the rain clouds were in the upper left, I adjusted the direction of the motion blur to come from the upper left.
The last thing I did was to add a layer mask to this top layer. I wanted to break up the rain a bit.
Make sure the default foreground and background colors are black and white.
With the layer mask selected I went to filter > render > clouds
If you are familiar with masks, you know that black conceals and white reveals.
So this mask of black and white broke up the pattern just a bit to make the rain look a little more realistic and resulting in this finished photo.