I talk about intakes on my Accord Cold Air Intake DIY so I won't talk much about theory here. The main difference for the STi is that I chose a short intake for two main reasons:
1) Intake temperature is not quite as critical on a turbo charged engine b/c all that compression of the air creates a lot more heat and the purpose of the intercooler is to keep that heat down. Some folks disagree, saying that every degree helps, but considering that most intakes for turbo cars are short suggests a general concensus. Of course, you can also purchase intake heat shields to promote intake of cooler air from the fenders instead of hot air from the engine bay.
2) Long intakes, such as those used in a CAI, have longer response times as there is that much more air to move when you open the throttle. Of course, compared to the length of tubing required for an intercooler (especially a front mounted intercooler) this is probably negligible.
This is a simple modification, even more so than the Accord b/c it's short and you don't have to worry about routing the piping. You could do this in 30 minutes with the right tools. You will need a flat head screwdriver, a Philips screwdriver, a 10mm socket, a 12mm socket and a long socket extension (12" recommended).
There are three parts: The short ram pipe, the air filter and the short ram support bracket (not shown). Ignore the large metal pipe in the picture, that's from the exhaust system.
First, remove the "ram air" intake (aka snorkel). There are two bolts that need to be removed using the 10mm socket (or a Philips screwdriver).
Once the screws are removed, pull up and to the right and the snorkel should pop out from the fender firewall.
Next, press the tab on the MAF sensor harness and disconnect it.
Locate the screw for the metal ring hose clamp and use your flat head screwdriver to loosen it until the hose clamp can be easily rotated around the main air hose.
Remove the two bolts holding the airbox down (12mm IIRC). The first one is fairly easy to get to with the socket extension.
Keep this bolt to hold down the short ram support bracket.
The second one is a bit harder to see but also easy to get to with the socket extension.
Gently remove the main air hose from the air box top. Also remove the three lines connected to the airbox (three arrows at top of picture), which can be done by hand.
Then unfasten the two tabs (left arrows) holding the top of the airbox down and remove the top.
Unscrew the MAF sensor (right arrow) from the top of the air box and transfer to the short ram pipe, keeping the same orientation and making sure not to damage the sensor.
Remove the bottom of the box as well.
You'll have to move some of the lines around but it will come out.
Install the short ram support bracket using a bolt from the airbox to attach it to the front most air box bolt hole. Leave it a little loose for now.
Insert the short ram pipe into the main air hose and rest on the support bracket. Partially tighten the hose clamp (right arrow)
Attach the air filter to the other end of the short ram pipe and partially tighten the hose clamp (left arrow)
Re-attach the MAF Sensor harness (middle arrow). Make sure everything is aligned to your liking then tighten everything and you're done!
Optional: reinstall the snorkel to help direct some cool air into the silencer which will feed the short ram. Alternatively, you can remove the silencer from your finder as well, but I chose to leave mine in place.