There are a few ways to do this. I recently did it in Carnegie Mellon's introductory proofs course. I'll try to outline here a few different solutions that various places have tried.
Carnegie Mellon (15-151): We alternated introducing new topics (usually via lecture) with what I called workshops. A workshop is during normal lecture time. Students are given 3-5 questions that range from conceptual questions to difficult proofs. We created the groups randomly, and we changed them every few workshops. We gave them whiteboards (you can buy big sheets of whiteboards at home depot for like $5 and have them cut them down for you) and markers, and asked them to work together on the proofs in order. As the lesson progressed, the TAs and I would walk around the room answering questions and reviewing proofs. Depending on how many resources you have this could be very difficult, but we decided to split the large lectures down into smaller ones so this was feasible.
MIT: Albert Meyer in 6.042 takes a different approach. The classes are still smaller, and I believe there are still "lab assistants" running around the room helping out, but he does the flipped classroom every lecture. He's done it in several different ways over the years. I believe originally, he gave mini lectures for the first 20ish minutes, and then the students worked for the rest. He might have moved to asking the students to watch the lectures at home--in a true flipped classroom format--now. One other thing to note is that the book Albert wrote is absolutely fantastic and completely open. It's a great resource for good problems, good explanations, and expository material for students to read.
Stanford: I can't remember the course number or name right now. I will do my best to follow up later by adding a link. Stanford takes a different approach than either of the other two. They have a standard lecture series, and sometimes, they offer workshops in the evening (which I believe are optional). This approach is particularly nice in the college setting, because it requires fewer resources and less contention for classroom space. Both of the CMU and MIT courses used a "special room" which allows for collaboration. At CMU, 15-151 is held in the CTC, and at MIT, 6.042 is held in the TEAL rooms.
There are other various strategies to do this, but these are the ones I've seen most commonly (and successfully) used for introductory proofs courses. Albert's resources are very useful, and I would be happy to share some of mine as well.