Have you already downloaded the image http://downloadmirror.intel.com/24355/eng/SDCard.1.0.4.tar.bz2 ? You need this image in order to use the Arduino IDE. For a more detailed explanation on how to connect your board and what software you need to install and how, take a look at the getting started guide here IoT - Intel® Galileo Board Get Started Guide | Intel® Developer Zone .
Once you complete this guide make sure you download the latest Arduino IDE version and select the proper board and COM port. This link may be of interest SD Card Setup and Sketch Persistent for Boards and Kits .
About Eclipse, take a look at IoT - Blinking an LED using C/C++ | Intel® Developer Zone . This guide has steps and an explanation of everything from install eclipse, blinking a LED to using sensors and more.
I think the "Arduino way" is the simplest way to start with, at least for simple projects.
If you think you can try one more... please describe the sequence (as thoroughly as possible) you follow so we can try to help.
Some simple "details":
a) I've used it in almost all Windows versions, not any Linux one, but I know it works too, at least in some of them.
b) In windows, the "best" IDE version would be 1.6.0
c) Before blinking, you should complete some steps as driver installation and COM identification. Anyway, if you describe the steps you follow we'll be (hopefully) able to identify the possible problems.
I've posted a reply in your thread GALILEO IS A BIG DISSAPOINTMENT, CANT EVEN CONNECT!. We want to help you, and it'll be helpful to have all your concerns in one place. Please continue the support in that thread to avoid confusions with your other posts that are all about the same issue.