Ok, I'll do my best to explain without pictures, and hopefully tomorrow I can take some for you. I can get you in the right direction, but from there you're gonna have to learn from yourself (the same way I did it).
First, follow the directions here for removing the first part of the center console:https://www.celicahobby.com/ubbthreads/thread.f_128156_0_collapsed_2__1.html
(you only need to remove the section with the ash tray and cig lighter)
Next, (with the shifter in N) you'll wanna go to the side of the shifter that faces the a/c controls. You should find two screws. Take them out with a Phillips screwdriver. Try to find the shortest one you can; if not, (with the car off) set the e-brake and shift it into 1, giving you more room to get a screwdriver in there (it's best to keep it in N though, or at most D).
The next part involves something I did on accident, and almost broke my shifter doing it. What you want to do is disconnect the main part of the shifter from it's base. You'll notice when pulling the shifter up that there's a metal rod and a wire. The metal rod is for pushing the shifter button, the wire is for your O/D switch. The picture at the end of this post (sorry about the size and the poor Paint chop) shows what area needs to be seperated. Be careful doing this, as you may brake the wire, and I haven't figured out how to fix that (fortunately I didn't break it). Carefully seperate these two pieces, and once you've done that, you should be able to lift the main part of the shifter up and off the metal rod.
Next, inspect the gray plate that sits on top of the black box (the area with the ovals for your shifter. If you look around the edges of it, you'll find it's fastened on to the black box by four plastic tabs. While in the drivers seat, face towards the passenger seat, grab the side closest to you, and pull towards you and up (don't try prying these open with a screwdriver; it's next to impossible, you'll probably just break the tabs). I found it useful to grab using the depressed area where the shifter moves; fingers there, thumbs on the outer edge. Once you get this side off, the other side should be relatively simple to take off. Be careful with the black plastic sliders; they'll be loose, though you'll probably have to end up adjusting them once you're done anyway.
Beyond that, you're on your own. I can look into this tomorrow if I have time. I wouldn't recommend trying to take apart the black box, because I don't know what's in it and you'll probably create more problems than you'll solve. You should be able to look inside where the metal rod is and see if there's anything gumming it up, and then carefully clean it up. If you pour anything over that thing, I'd recommend giving it a dose of WD-40 when you're done, because there are some lubricants that are already there (unless anyone has a better suggestion besides WD-40).
Again, do this at your own risk. If you don't feel comfortable doing it on your own, take it to a qualified mechanic.
EDIT: credit goes to the Ecelica photo gallery for the original photo.