Here is a short summary of what happens in part 4. 
This is really all you need to know, you aren't missing much.

Han convinces scientist Qwi Xux of the evil her creations are used for, 
causing her to help steal the Sun Crusher and defect with the escaped prisoners.
 
Kyp uses his latent force abilities to guide the ship around a maze of black holes 
where they run into the relinquished Millennium Falcon, piloted by Luke and Lando.
 
The pursuing fleets of Kessel and Maw Installation are left to battle each other.

Meanwhile, Leia and Mon Mothma select the moon Yavin 4 as the location for a new Jedi academy.
 
Luke is pleased with the selection, and invites Kyp Durron to join in future training.