ICQ is still around. There are also YahooIM, AOL IM (AIM), and MS Messenger. All are free to use. To use any of them, you need to create an account. And you have to use the same program as whomever you wish to communicate with. For example, if you have an ICQ account, you cannot talk to someone on AIM.
To create accounts:
For YahooIM, you can just create a Yahoo email address.
AIM, the easiest thing is to go to http://www.aim.com/ and sign up through the site.
For ICQ, go here: http://www.icq.com/register
For MSN Messenger, you can go to http://www.msn.com (the link to messenger is there somewhere).
MS Messenger comes pre-installed on WindowsXP, and the other services require downloads.
However, I would suggest avoiding using the MS Messenger application, due to numerous security issues with it.
One of the best options is to use Gaim, which is a program that supports all four messengers (you can use all of them simultaneously, with only one application). It is a small download, it is opensource (free), and very easy to use. By 'easy', I mean that my mother was able to figure it out in about one minute, and she has difficulty playing a CD in the computer (I am not exaggerating).
To find Gaim, go to http://gaim.sourceforge.net and go to the Downloads section.
If you have any more questions, just post here or PM me.