I first discovered infrared film as a high school photography student and loved its surreal, beautiful, and unpredictable effects. As a digital photographer, one can't use infrared film, but there are a few other options to recreate the effect digitally.
(1) You can recreate the effect in Photoshop, though I have yet to see the effect recreated perfectly using this method. Generally this involves converting your image to black and white using mostly the 'red' channel and applying glow and grain to the image.
(2) You can replace your dSLR's sensor with an infrared sensor; however, this is expensive since you need another camera body and have its sensor swapped out. You can learn more about this process
here.
(3) You can use an infrared filter. This is the method that I decided to try out, and I purchased a Hoya 72 Infrared Filter. I've tried it out a few times and haven't been too impressed with the results, but I'll keep trying to iron out the kinks. I shot the image below of the LA skyline.
[click image to view larger.]
For comparison, here is an image I shot with real infrared film on a manual SLR back in the 1990s. The filter seems to create very grainy images without the lovely soft glow of the infrared film. I'll work on recreating the true effect in Photoshop and keep you posted :)