I will present two orders here, chronological order and the order in which they should be read.
#Order in which they should be read
This is mostly in chronological order, but it's ordered more in how they came out and how they will make the most sense. When there are 5/3 books just listed in order, that's the order that the series goes in.
Percy Jackson and the Olympians
First comes The Lighting Thief.
Then comes The Sea of Monsters.
Then The Titan's Curse.
The The Battle of the Labyrinth.
Then The Last Olympian.
This is the original series; therefore, it should be read first.
Now you should read the short story collection The Demigod Files, as most of the stories take place during/after PJO.
The Heroes of Olympus
First is The Lost Hero.
Then The Son of Neptune.
Then The Mark of Athena.
Then The House of Hades.
Then The Blood of Olympus.
This is the sequel series to PJO, and is a continuation of the stories.
After this would be a good time to read The Demigod Diaries, a collection of short stories, which have stories from HoO.
That's the obvious part, as those are all in one universe. Now..
The Kane Chronicles
First is The Red Pyramid.
Then The Throne of Fire.
Then The Serpent's Shadow.
These are sort-of in the same universe, see the other question, but they are with entirely different characters. The series makes several references to PJO, though, so read that first.
Now, you should read the crossovers, as they only make sense if you've read KC and PJ:
First is The Son of Sobek.
Then The Staff of Serapis.
Then The Crown of Ptolemy.
Now, you should read The Trials of Apollo and Magnus Chase and the Gods of Asgard together, as they take place at the same time and may have spoilers if not read together.
This is as in chronological order as I can figure out, based on the books that are out:
First is The Trials: The Hidden Oracle.
Then comes Magnus: The Sword of Summer.
Then Magnus: The Hammer of Thor.
The rest haven't come out yet.
#Chronological order
The Demigod Diaries: The Diary of Luke Castellan.
PJO: The Lighting Thief.
PJO: The Sea of Monsters.
PJO: The Battle of the Labyrinth.
Files: Percy Jackson and the Stolen Chariot.
Files: Percy Jackson and the Bronze Dragon.
Files: Percy Jackson and the Sword of Hades.
PJO: The Last Olympian.
Diaries: Percy Jackson and the Staff of Hermes.
Diaries: Son of Magic.
Kane: The Red Pyramid.
Kane: The Throne of Fire.
Kane: The Serpent's Shadow.
HOO: The Lost Hero.
Diaries: Leo Valdez and the Quest for Buford.
HOO: The Son of Neptune.
HOO: The Mark of Athena.
HOO: The House of Hades.
HOO: The Blood of Olympus.
PJO/KC: The Son of Sobek.
PJO/KC: The Staff of Serapis.
PJO/KC: The Crown of Ptolemy.
Magnus: The Sword of Summer.
Trials: The Hidden Oracle.
Magnus: The Hammer of Thor.
...And the rest of The Trials of Apollo and Magnus Chase and the Gods of Asgard haven't come out yet.
All information in this answer came from my own reading of all of these books.
The top order has been made depending on how the information has been given, such as the introduction of characters, plot points, etc. This ends up mostly being in the order that Rick Riordan released them in, with a few minor changes that take into account later books.
There are a few stories that I didn't include here, these being Percy Jackson's Greek Gods, Percy Jackson and the Greek Heroes*, and the stories included in the app.
The Gods/Heroes can be read at any time, as they are the ancient Greek legends, not part of Percy's story. The stories that come with the app aren't necessary for the others, but if you want, read those any time after PJO,as that's what you need to understand those.