I have heard Portugal really made huge technological, societal, economic and political moves that made them ground breakers and drivers of this trade, how is this the case?
One of the most important sources for understanding the Trans-Atlantic slave trade is the Slave Trade Database: http://www.slavevoyages.org/
A look at the statistics for Portugal/Brazil show that during the slave trade, a full 3,897,000 slave embarked from Africa on ships with a Portugal/Brazilian flag. Over 3,483,000 slave disembarked. This makes Portugal/Brazil the number one country for the transportation of slaves. Number two was Great Britain with and embarkation of 3,092,000 slave and a disembarktion number of 2,604,000 slaves.