help me out?

Ok.. may be there is other way around but you can do this by..following method.
Chat with one person and close all other chatting. Close other internet related stuff too (just for making things easy).

Then on command line type :

It will list all connection to and from your computer. See connections from yahoo and then you can easily figure out which one is that person.
If still it is not happening then transfer a small file between u and that person then run "netstat" !

Well Husna, If you just need to know whether a person is using different ID's to chat with you, You can do this by the method told by Ricky, there are some softwares also designed for this purpose. But if you want to know hacking n cracking Yahoo Id's, It's something that only professionals can do. I mean, for a beginner like you it will take not just extensive hard-work but years. Hacking is not something that can be learnt by reading books, each n every hacker has his own ways of doing things that might not not work with others....