As someone who took part in the D&D Next public Alpha/Beta materials, I remember filling out a survey before the first materials were released asking what I liked/disliked most from each edition. From there, they would gradually release digital playtest kits, which generally consisted of prefabricated characters and a quick-start rules packet. Once released, they had a webpage to log in to submit feedback on the latest release.
Playtesting itself was on an individual basis. You were provided the materials and expected to run them with your own players. To my knowledge there were no formal playtesting sessions for the public run/hosted by WotC.
The first batch of files (Around 5/22/12) themselves were a very limited module called Caves of Chaos with prefabricated characters including a high elf wizard, halfling rogue, dwarf fighter, a mountain dwarf cleric, and a human cleric.It included a "how to play", and a quick start guide for DMs, as well as a Bestiary file for the monsters in the module. All of the class abilities were on the individual characters.The characters could be upped to level 3 as they adventured with specific tracks listed on each one. Monsters at this stage gave a raw XP number and CR was not a factor. The survey ran 5/31-6/13.
The next survey opened 7/18 and asked for feedback on wizard and cleric spells. From here the surveys were open ended but you could only access each once from your account.
More playtest materials were released 8/22/12, and focused on added sorcerer and warlock, and allowing characters to get to level 5.
Another survey was opened 9/14/12 for races, backgrounds, specialties, spells and monsters.
On 10/8/12 a playtest packet including a revised version of the original module, magic items, and monster tweaks was released.
A survey was later opened on 1/10/13 focusing on rules, classes, maneuvers, feats, spells, and high level play.
On 1/29/13 materials were released for all levels of the Barbarian class and a batch of rules to convert D&D Encounters sessions for D&DNext. It was announced in that message that starting 2/6/13, D&D Encounters would support Next as well as 4e.
The last batch, 9/19/13, was a lot more expansive and more of a beta to the D&D5e we know now. Bards were added, classes had a pair of paths, there was technically information available to get to level 20 and included an editable PDF character sheet. That batch included everything you would expect from a quick start box and more modules to try.
The final communication I have is from 12/11/13 stating that playtest materials would no longer be available after 12/15/13.
D&D 5e was released in July of 2014.