We've heard talk of Team Builder Draft, and while we've gotten some details, a lot has remained unclear. Today, Riot Lyte went more in depth on his ask.fm to give us a pretty clear idea of exactly how this will play out (I've made some minor formatting edits, but all text is presented verbatim):

Been getting this question a lot recently, so going to compile all the current information into 1 post.

History:
We learned a lot from the original Team Builder launch, and although the queue had better player behavior (lower reports, lower leavers/AFKs, lower Champ Select conflicts, higher honors), queue times were a major issue. We also saw a demand for no mirror matches, and a "draft" version of Team Builder that incorporated picks and bans.

Current:
Although players have been asking for a Team Builder "draft" since the original launch, we spent some time filtering down all the lessons we learned from the original launch and did a fresh design for Team Builder Draft while working on other features like LeaverBuster, Instant Feedback, Party Rewards and more. We started work on the new Champ Select earlier in 2015, and have begun internal testing the system with some players and pros to get their feedback. We're pretty confident in the new experience, and now intend for this to be the new Champ Select experience for some queues in the future assuming the feedback continues being positive after launch. Side note for a second, there's a pretty fun moment in the new Champ Select experience where most of the players in the last playtest did a collective "Ooooo." So, we're curious to see what the rest of the playerbase thinks as well.

Our main design philosophy of the new Champ Select was to retain as much of the player behavior benefits as possible, while drastically reducing queue times. We also wanted to retain the strategic elements of drafting. This philosophy led to us to getting rid of the "Captain's Mode" where you can accept or decline potential teammates, getting rid of mirror matches, and no longer asking players to choose a Champ prior to Champ Select.The new Champ Select flow is now:

1) Players can invite friends into a Lobby.
2) Each player is required to select at least 2 Positions (such as Top/Mid, or Mid/Jungle). On average, Ranked players only play 2.2 positions, so we wanted to start simple with a Pick-2 design, but have some backups like rank-sorting all 5 positions if there are queue time issues. We also have designs to incentivize mastering all positions in the future.
3) There's a new position called "Fill."
4) We're currently asking Duo Queues to cover at least 3 unique positions, to further improve queue times. Duo Queues will still have a higher chance of getting the exact 2 positions they want, but it is not 100% guaranteed.
5) Once you've chosen your positions, we match you into a full team and you enter Champion Select.
6) We've made some changes to how drafting works; however, we'll be talking more about this in a future design blog. 
7) During Champ Select, you can still negotiate with your teammates to lane swap or trade champs if you want a more favorable match-up just like Champ Select today.
8) Once drafting is done, your team enters the game.

Lyte has now painted us a pretty clear picture of how the new system will work, and it sounds like they more or less have things ironed out. I'm certainly curious to see what the new champion select will look like, and particularly as to what that "oooo" moment was. If you have any speculation, leave it in the comments below!