How to display 1 full article and the a summary of others
Install Views, then enable the disabled view called Front page. 

To get two different view modes for the nodes, you could add an attachment display to the view that shows a single latest article in full view mode and add it to the view at the top. Then you would set the page display (the original view) to display teasers, starting at an offset of 1.

It could also be accomplished with Display Suite.