Please note and read the system requirements for all downloads.
Nothing I can do to help you install these if you are running on a
Millennium Falcon vintage computer. Before you get too far ahead you
will have to download and install Microsoft Netframe 3.5 SP1
before downloading and installing ArcGIS Explorer. The alternative,
especially if you are operating in Windows 7 or 8 is to check out this article, which shows you how to setup Netframe 3.5 that may already be part of your OS.
The most recent edition of ArcGIS Explorer that I have last seen was Build 2505.
I no longer have any issue trying to install it on my spanking “brand
new” Windows 8.1 system now that they have updated it for 8.1.
Once you are done, you should have something that looks vaguely like the Icon on the left on your desktop.
Click on that icon launching ArcGIS Explorer and you should get a screen that looks like the screen capture to the immediate left.