Okay, double click the install program, this will open up the program package as well as pt the drive icon on your desktop, in the program package you'll see the program icon (I think it might be the MSM Messenger guy -- haven't done this recently so not sure), drag this icon into your application folder (command+shift+a should open the applications folder).
If you do this correctly you'll see a dialog box showing the program is installing, you can then run the program from there (or drag and drop the program into your dock). If it runs you can remove the .dmg file as well as the drive that appears on your screen.
For a visual on this check out this article:
Installing DMG Files. As full disclosure I wrote that article and the sample shows doing it with Firefox but the steps should be the same.
Any more questions feel free to ask.