This is the official order, as copied from the table in "The skies of pern".
01 - DRAGONFLIGHT
02 - DRAGONQUEST
03 - DRAGONSONG
04 - DRAGONSINGER
05 - THE WHITE DRAGON
06 - DRAGONDRUMS
07 - MORETA: DRAGONLADY OF PERN
08 - NERILKA'S STORY
09 - DRAGONSDAWN
10 - THE RENEGADES OF PERN
11 - ALL THE WEYRS OF PERN
12 - First Fall
13 - The Dolphins of Pern
14 - Red Star Rising (published in Us as Dragonseye)
15 - The Master Harper of Pern
16 - The skies of Pern

This can get confusing :-).

Dragonflight, dragonquest and the white dragon form a triplet. I would call it a trilogy, but that implies independance. They are very much part of the rest of the pern series.
Dragonsong, dragonsinger and dragondrums form another triplet with simplier plots, sometimes refered to as the "Harper Hall" Trilogy. But those two triplets actually follow different characters at the same time, so there is some overlap. I suggest reading them in the order from the table. However you read them, start with dragonflight. You wont understand the rest without that background. After the initial six, they progress in the simple order above.

To make things more complicated, Moreta is set at least 400 turns before most of the others.  Nerilka's Story is set simutainously but follows a different character. Renegades appears to be set all over the place and time. I havn't read it yet, but a brief look shows it ends exactly as Weyrs begins.

It gets better. Dragonsdawn and First Fall are set about 2500 turns before the others!

Finally, the titles can also get messed up. Some books have different titles in the US and UK, and they are often refered to by their subtitles.

"The cronicles of Pern" is the same as "first fall".
"Red Star Riseing" was also published as "dragonseye" and is subtitled "The second cronicles of pern".
"The Renegades of Pern" is also "Dragons kin".
"On Dragonwings" is a three-in-one book of Dragondawn, Dragonseye and Moreta.
"Get off the unicorn" is a collection of shorts (I think), which contains bits of pern as well as of other series. The same applies to "The Girl who Heard Dragons". I think. As I said, this is a very confuseing series.


There are some short stories which are not set firmly in the series.
I found "Weyr Search" on a p2p network. "The Smallest Dragonboy" is a short story frequently seen in junior school textbooks.