I'll assume you have a Definity, as you are posting here.
Or I think it's called Multivantage or something now.
In any case...
As RFWatts stated, you need to have a MAPD board. This is like a network board for your pbx, although it does more than that.
You'll now need some sort of CTI software to talk to the MAPD board. There are several ways to do this.
1. Use a CTI server software. this will essentially act like a communications server (similar to a windows driver), that will talk to the pbx. Two that I know of: Avaya CT and IBM Callpath.
With the CTI server, you can then buy software that is compatible with the CTI server you bought.
So this solution requires you to have
a. your pbx
b. the MAPD board
c. the CTI server
d. the application you buy that is compatible with the cti server
e. everything the application requires to run of course.
2. An alternative to the above mentioned solution, is to get the CTI server and develop your own. I know that the Avaya CT server comes with an SDK with C APIs that you can use to build your own CTI application. We've done this, and though it's time consuming, it gives you the flexibility to do what you want.
3. Buy a CTI application that can talk strait to your phone switch. I think Avaya had some, AvayaCRM or something, but I'm not very familiar with this route.
I've done 1 and 2.
Hope this helps.