Now that you have the intake out, you can see all the junk that is inside of it. I used a long flathead screwdriver and a hammer to get most of it out. A dremel comes in handy as well, especially for finishing off little bits here and there. Basically, you want to take out all the fin thingies, as well as the big rounded part towards the front of the intake (the thing with the 2 holes on the back side of it). Be careful and take your time, as I'm sure you don't want to punch a hole through your intake.
I started from the back end using my nice long screwdriver that was able to reach almost all the way through the intake. I just carefully place the screwdriver where I wanted to start breaking stuff, and carefully hit it with the hammer. I noticed that fins and whatnot aren't glued or anything to the intake, but they're sitting inside channels and grooves, so after a point they come out easily.
The front rounded part was the most annoying. I found it a little easier to get the edges of the rounded part out after I started breaking off the little channel it was sitting in. For the most part, the channel broke off flush with the intake. Just keep working at it until you've pretty much cleared it out.
Once I got everything busted out, I used the dremel to help smooth things up. I mostly just used the barrel sandpaper attachment. Some of the spots are annoying to get at, just do the best you can to clean things up in there. Once you're finished with that, make sure you get all the loose junk and bits of fiberglass out, as whatever remains will get sucked up to the filter.
The last thing I did was to break off the two pieces on the bottom of the fairing stay that stick down inside the intake. They break off quite easily, I just pushed where the arrow is towards the outside of the stay. Ideally, you'd probably want to make some kind of block off to put in the intake, but the stay should still "seal" up with the intake, as the pieces you're breaking off aren't what actually make the "seal". (I didn't make the block offs cuz I didn't have materials too. At some point I'll prolly get back in there and do them though.)
Now just put everything back together. Bolt the intake back up, and bend the metal clips back over the bolts. Put the stay back on the intake, put the headlights back on, reconnect the electrical connectors, and put your plastics back on. All done!