I vaguely remember replacing the ignition switch in a '78 Corolla that my sister used to own; it was relatively easy, even for a novice.
On most full-size American cars, the steering column is built like a big metal tube, with everything loaded in from the top; if you want to get at/fix something in the middle, you’d have to first remove the steering wheel and take out all the other stuff, roughly speaking.
Luckily, your car is in no way built like that, so this will be very easy. Trust me; just do it yourself and save some money, you probably only need a screwdriver or two.
You’ll see that just behind your steering wheel, the keyhole, turn signal lever, and wiper switch are “wrapped” in a piece of plastic. Upon closer observation, you’ll notice that this is kind of a clamshell deal, with a separate top and bottom piece. This is held on partially by snapping in place, and partially by some screws you can get to by looking at it from underneath.
Undo the all the screws you can find, and then gently pry on the shroud, so you can discover any missed screws, as well as ascertain if the two pieces also snap together. The WORST that will happen is that you’ll cosmetically crack it; it’s not a vital part of the car. Just be patient, though, and you won’t break it.
As an example, here’s a picture I took recently of a 2003 Corolla’s steering column, with the shroud removed:
Your car will look just slightly different, but not by much. See the big metal part that the key is going into? That’s the ignition LOCK, as Gary T points out. You do not need a new lock. Just at the back of the lock, see the white plastic piece, with the white plastic plug with wires coming out? That’s the switch itself, which has worn out on your car. It will come out with a couple of screws, and then you unplug it. If yours doesn’t have a plug right on it, follow the wires a foot or so; you’ll eventually find a place to unplug it.
If you have a good amount of spare time, and you like to learn stuff, and you want to save a few bucks, buy your switch from a junkyard where you pull out your own parts. You’ll feel a lot more confident taking the junk car apart, then you’ll better know how to do your own. Don’t forget to also take the screws you removed from the junk car, so you’ll have extras.
Otherwise, it’s probably simplest to just buy a new switch from a Toyota dealer.
If you’d like to see more pictures of a disassembled 2003 Corolla, including all the wire colors necessary to install an alarm, you can read my info here
So don’t worry; it’s just a small amount of money, a half hour of your time, and maybe five screws. Just go ahead and do it; let me know if you get stuck and need advice or anything.