The referenced links were as follows:

Review the Apex Developer guide and in particular the section which explains Apex classes: 

http://www.salesforce.com/us/developer/docs/apexco​de/Content/apex_classes_understanding.htm

and the one which compares Apex to Java:

http://www.salesforce.com/us/developer/docs/apexco​de/index_Left.htm#StartTopic=Content/apex_classes...

and the one which explains triggers:

http://www.salesforce.com/us/developer/docs/apexco​de/index_Left.htm#StartTopic=Content/apex_trigger...

The documents are very good.

However I'm still a bit confused by something.  I have created a class just to test out some basic Apex functions. I have one method within which I test out the functions. I also have a static method in which I create an instance of my class & from this instance call the method (within which my functions exist).  I have no SQL updates & do not want to interact with any stored objects (I just want to get familair with functions so I'm giving dummy string values etc...)

My code compiles correctly so that is all good. I'm wondering though how I can I then run the class to test what happens. I have some System.debug functions used & I'd like to see the output.  As I am developing this on my sandbox it is not for production use.

If I click on "Run" from the Force.Com IDE menu it then has option for "External Tools", In which there are options for "Run As", "External Tools Configurations", and "Organize Favourites". The "Run As" option's sub option is greyed out.

As I have no DB interactions & no requirement to interact with any objects I don't think I need to use a trigger to invoke my class (from reading the documentation triggers seem to interact with DB calls). Other class invoking options I see are to use a Scheduler, Anonymous Blocks or AJAX.

If running a similiar Java application/program in eclipse I'd just choose Run As -> Java Application.

i guess this may be due to my lack of familiarity with cloud based development, but how do I actually run my application to see the output? 

Any suggestions would be welcome & apologies for my lack of understanding on this (even after reading the docs).

Thanks in Advance!