How are Assassin's Creed 1 and 2 related to Assassin's Creed 4?

The first six games in the series⁽¹⁾ follow the genetic heritage of Desmond Miles, who is the protagonist in the overarching framing story which is set in 2012, which is narrated throughout these games through vignettes set in present times.

In each game, the player takes up the role of another ancestor (Altaïr Ibn-La'Ahad in Assassin's Creed, Ezio Auditore in Assassin's Creed II, Brotherhood, and Revelations, and Edward Kenway in Assassin's Creed IV: Black Flag).

A quick sketch of the series' premise (containing very mild spoilers):

Desmond Miles is the youngest descendant in a lineage of assassins. He is abducted by Abstergo Industries, a pharmaceutical company that forces him to take part in a highly secretive project. He is put into the Animus, a neurologically controlled virtual reality machine that makes Desmond relive the lives of his ancestors. By 'browsing' chronologically through these genetic memories, Abstergo hopes to find the Pieces of Eden, ancient relics said to harbor divine power.

For more information, check the Wikipedia page on the series, read up on the overarching story on Den of Geek, or watch it as it is explained to you by Polygon, or, more extensively, by LazerzZ.

^{(1): Assassin's Creed, Assassin's Creed II, Assassin's Creed: Brotherhood, Assassin's Creed: Revelations, Assassin's Creed III, Assassin's Creed IV: Black Flag}