I don't think you have been trying for ages
Desktop is the place that's visible on your screen if you're using one of these desktop environments like KDE, Gnome or XFCE..as a directory path it's ~/Desktop
(usually). Or in the long format, /home/yourusername/Desktop
. Programs -- what do you mean by that? There is no certain place for programs (like C:\Program Files\ under Windows), parts of programs are usually installed in different places (libraries in their own place, binaries in their own place etc.)
If you are looking for binaries, executables, try /bin
How did you intend to install this "messenger" (and do you mean Gaim, Kopete, aMSN or some other 'messenger')? If you are using a distribution with a binary package manager (one like Fedora Core, SuSE, Ubuntu, Debian, ...), it's preferrable to install the program using the distribution's own package manager application (be it yum, apt, yast or whatever), if possible, rather than manually download it and so on; package manager handles automatically dependencies etc. so it's usually easier than doing the thing manually.
Next time you post, try to include more information; for example in this thread you could have told which 'messenger' you were trying to install (the name of the program), where you downloaded it, in what format was it (.rpm or .deb or .tar.gz or which file type?) and so on. And especially you should tell which distribution are you using; it would be wise to add it to your profile so it was visible all the time, but at least tell it in your posts.