We are a small software development house and wish to explore the
option of engaging third party suppliers and developers to provide a
more flexible and cost effective resourcing base.

I wish to learn more about engagement with suppliers and overseas
("offshore") developers? 

What does 'engagement' with third parties mean? 
What does 'outsourcing' mean? 
(I have my own understanding on these 2 terms but what do other say out there?)

Many companies have outsourced development work to India/Mexico and I
am looking for an overview of this as an industry as well as case
studies and any approaches or
methods.

Any information you can find on the web such as advice, best
practices, methods & approaches & processes to engage third parties
(especially third parties which are offshore developers) would be
useful.

Please identify typical pitfalls or dangers involved - common
problems, mistakes made.

I realise this is a broad subject so take a broad approach on software
development and outsourcing and narrow it down to the different
approachs and specifics. 

N.B. This is all in the context of software development.

Thank you