The last episode of the anime, 1076, adapts chapter 1049 from page 2 to 17. Then the story would continue on page 2 of chapter 1050, this is the chapter of the manga after the anime, it corresponds to Volume 104 that collects the chapters 1047 to 1055.
Compared to other animes, One Piece adapts very little material from the manga, due to the fact that the anime's story is close to the manga's. Pretty much if we start reading the manga where the anime ends, we would only read 43 chapters to keep up with the manga.

The last chapter of the manga is 1092, and the last volume is 105 that compiles the chapters from 1056 to 1065, this in case you want to buy the corresponding manga volume. In the following table, I will summarize the equivalence between anime and manga:
LAST EPISODE (ANIME): | CHAPTERS (MANGA): | VOLUME: |
---|---|---|
1076 |
Chapter 1049 (p. 2-17) |
Volume 104 (chaps. 1047-1055) |
The anime is on the air, with a new episode premiering every Saturday night, with the exception of Japanese holidays. The manga is also being published, they come out every Thursday and you can read it for free on Sundays through Manga Plus.