1) I'm not a capologist but I'll do my best and would appreciate any additions or corrections from knowledgeable nontrolls.
2) We trade for Butler and max Durant and Horford.
3) Our four stars (Thomas plus the three new guys) would be approximately $76 million of the probable $92 million cap.
4) The trade for Butler would be Crowder, Bradley, Young and #3. This is an overpay but allows you to get Horford and Durant here. The cap situation probably won't allow you to keep either Bradley or Crowder.
5) We have to let Johnson, Jerebko, Turner, Sullinger, Zeller, and Holland (bet you forgot about him) just walk.
6) That would leave about $11 million left in guaranteed salary: Smart, Olynyk, Hunter, Rozier, and Mickey. This would give us 9 total players for $87 million and $5 million left to sign draft choices and fill out the roster with minimum wage guys. If that's not enough we can always move someone like Olynyk for a future draft choice, though I prefer not to.
7) The cap will go up again next year which will allow us to fill out our rotation with some veterans plus Brooklyn 2017.
This is, of course, based on the idea that Durant would come here if Butler and Horford are brought in. That idea may be entirely false. 
I've worked it out where you can get away with it just being one of Bradley/Crowder, Rozier, Hunter, and Young after signing Durant and Horford with capspace, though that'd assume that Durant would be okay as a small-ball 4 here.
FYI, I just looked at what the salary situation would be if we did the "rumored" (not actually rumored, but just a trade idea someone came up with on bleacherreport) Jimmy Butler deal.
The trade idea has us giving up Bradley, Jerebko, Rozier, #3 and #16
It actually would make sense. You kind of need to include Bradley in such a deal, because he makes more money than anyone on the team (8+ mil) and you'd have to match salary to preserve max cap space.
Here's what the salary situation would look like afterwards:

So this deal would leave us with roughly 50 mil in cap space. With max contracts 25 mil each, we'd be able to bring in Durant and Horford.
But you'd have to renounce the rights to Zeller, Sully, Amir, and Evan Turner.
So really, you're losing #3, #16, Bradley, Rozier, Jerebko, Zeller, Sully, Amir and Turner. A lot of those guys played significant roles for this team and who knows how good #3 and #16 could end up being.
You're potentially gaining Butler, Durant and Horford.
Obviously, it makes us a better team. PG - Thomas/Smart, SG - Butler, SF - Durant, PF - Crowder, C - Horford
Nobody is going to be disappointed at that, obviously. Just be prepared to say goodbye to a lot of familiar faces and some "what-if" draft picks in the process.
It's 100% worth it if it results in Kevin Durant.