On the FIRST DAY OF PASSOVER we read from the book of Exodus (12:21-51) of the bringing of the Passover Offering in Egypt, the Plague of the Firstborn at the stroke of midnight, and how "On this very day, G-d took the Children of Israel out of Egypt."
The reading for the SECOND DAY OF PASSOVER, Leviticus 22:26-23:44, includes: a list of the moadim -- the "appointed times" on the Jewish calendar for festive celebration of our bond with G-d; the mitzvah to Count the Omer (the 49-day "countdown" to the festival of Shavuot which begins on the 2nd night of Passover); and the obligation to journey to the Holy Temple to "to see and be seen before the face of G-d" on the three annual pilgrimage festivals -- Passover, Shavuot and Sukkot.
The readings for the four INTERMEDIATE DAYS OF PASSOVER include:
1) Instructions to commemorate the Exodus by sanctifying the firstborn, avoiding leaven and eating matzah on Passover, telling one's children the story of the Exodus, and donning tefillin (Exodus 13:1-16).
2) A portion from the Parshah of Mishpatim which includes the laws of the festivals (Exodus 22:24-23:19).
3) A section describing Moses' receiving of the Second Tablets and G-d's revelation to him of His Thirteen Attributes of Mercy, which likewise concludes with the laws of the festivals (Exodus 34:1-26); when one of the "intermediate days" of Passover is Shabbat, this is the reading read on that day, and it begins 12 verses earlier, with 33:12).
4) The story and laws of the "Second Passover" (Numbers 9:1-14).
On the SEVENTH DAY OF PASSOVER we read how on this day the sea split for the Children of Israel and drowned the pursuing Egyptians, and the "Song at the Sea" sung by the people upon their deliverance (Exodus 13:17-15:26; full summary with commentary here).
On the EIGHTH DAY OF PASSOVER we read Deuteronomy 15:19-16:17. Like the reading for the second day, it catalogs the annual cycle of festivals, their special observances, and the offerings brought on these occasions to the Holy Temple in Jerusalem. The Eighth Day's special connection with the Future Redemption is reflected in the Haftorah (reading from the Prophets) for this day (Isaiah 10:32-12:6).