The cheapest way is as a 2D overlay using a texture with alpha. If you are using Photoshop, use a process similar to the one described in
this video to create the texture. Of course, you would ignore the animation and scene set-up stuff in the video (you are just after the tileable rain mask). You want to use the mask to generate a texture with degrees of alpha, rather than applying it to a photo (similar to the way I made the glow and smoke textures, which I've described in other threads here -- I can give you a step-by-step if you are not super familiar with the Photoshop menus). Once you have the tileable texture, the cheapest way to animate it is to incrementally change the u/v coordinates to make the rain fall downward. Another option is to animate it with a texture effect (slower in my experience).
If this isn't realistic enough for your project, I am working on a method that incorporates the rain as either particles or planes into the 3D scene, but I haven't yet found a way that is both cheap and looks believable. I'll be sure to post an update if I can figure out a good method.
