Life was simple with Exchange 2003 but as life goes on, newer versions of Exchange have appeared and what was once simple has become a bit more complicated.

One of the first gotchas you notice with Exchange 2007, 2010 and 2013 is the increased security and the challenges of connecting to Exchange remotely.  One tool that I find to be invaluable is the Microsoft Remote Connectivity Analyzer which can identify various issues with your configuration.

https://testconnectivity.microsoft.com/

I have used this tool on numerous occasions but for those who are using it for the first time, I would suggest selecting the option to "Manually specify server settings" in order to keep the setup simple.  When you get the hang of it, this will make more sense but for now, just trust me.