Hi Brian,
First of all, let me start by saying that the Environment is the single most complex window in Logic. It's like MAX, or any other "graphic oriented programming environment." You're not simply "turning on a module" you're "wiring" one widget to another, like constructing a small 2D replica of a hardware studio inside Logic.
Think of it like you're physically carrying a 20LB rack mount box called an "arpeggiator" and getting out physical cables and wiring it up to a reel-to-reel tape deck (and if you're not old enough to have ever used one of those, PLEASE don't tell me, I'll feel ancient! 🙂 ). The Environment is a very old aspect of Logic, and it's been around since the days when people actually used large physical devices and recorded on tape, and it still contains the graphical equivalent of it.
If you want to learn more about the environment, I recommend reading the manual, going to Len Sasso's swiftkick.com and downloading his free Environment Toolkit PDF, or buying a book such as Logic Pro 9 Power (which I co-wrote, and wrote the Environment chapter).
Now then: In Logic, you have the option of connecting the arpeggiator object to the entire sequencer (as Eli showed you) or to a single instrument (either MIDI or Software).
If you wish to connect the arpeggiator to a single instrument, what you would do is:
1) Add the software instrument to a software instrument channel
2) In the environment, open the Mixer
3) Under the software instrument channel in the environment Mixer, create an Arpeggiator object
4) Drag the little cable thingy from the arpeggiator object to the software instrument channel with your software instrument. This is the software equivalent of taking your physical arpeggiator box and plugging it into your instrument in your physical studio.
Then you'd click out of the Environment window and back into the Arrange, where you'd need to create an Arrange track and set it to the Arpeggiator object you just created. This will work like the Guitar Pro arpeggiator in the sense that the arpeggiator is a PLAYBACK EFFECT. It doesn't actually alter the recorded notes, it alters what is played back when you hear the instrument. This is good in that if you want to change your original chord, you can, and the arpeggiator will perform as you expect on the new chord.
If you want to adjust the parameters of the Arpeggiator, go into the Environment window, select the arpeggitator object, and you'll see a list of parameters you can adjust. Note that you can also change the name of the object, so instead of "arpeggiator object" you can name it "FM8 groovelator" or whatever you like.
Since the arpeggiator is a MIDI effect, you CAN NOT use it to process audio tracks like a plug-in effect, only MIDI.
As I said, the Environment is certainly not easy to understand and is incredibly deep. I hope I was able to give you some basic help, but I highly recommend reading up on it if it interests you. And it can be fun-I created a "Superarp" which is a lot of fun! (doesn't work in the current version of Logic though, it was created in Logic 4).
Orren