That depends on a few things. First off, your frame on the floor doesn't mean a thing. At this point, in order for ANYONE to help you, you need to help US, by telling us everything you can.
1. Is this an apartment, or an upper room in a home?
2. What kind of existing floor STRUCTURE...ie...concrete or wood.
3. What room is below...bedroom? kitchen? family room..???
4. Where would you cut the materials...ie...framing and SHEETGOODS? And how large is the space(just lifting a sheet of 3/4"MDF or 5/8" sheetrock is a chore. Laying it out to cut and manuver can be a lesson in hindsight?
5. How? What tools do you have to machine these parts and materials?
6. Any construction or fabrication experience?
7. Can you read blueprints or plans? Do you understand section and details on drawings?
8. Where is this going to be assembled? How large is this space and where in the room is it going( ie...middle of the span places a larger percentage of the load on the support joists themselves rather than the walls that support them.
9. What kind of budget do you have? I can guarantee this will run about $1000, with framing, sheithing, caulking, hardware, door/jamb/latch/ threshold/ seals, insulation, absorption material, fabric, electrical, and....the biggie. Ventilation fan, ducting and grills, which we haven't even discussed yet. The fact is, when you "soundproof" an envelope, you "airproof" it as well. Singers like to breath.

Not only that, people and lighting generate HEAT very quickly in an insulated and airtight enclosure. Therefore, you need to PENETRATE the leafs in such a way as to SUPPLY and REMOVE air at the same time, WITHOUT generating a flanking path for fan noise through the ducting. Not only that, where you place the fan unit has a direct bearing on your ductwork length, geometry, and air source. I can hear what you are thinking right now...I don ned no stinkin fan!!

Well, maybe YOU don't. But since you haven't told us anything about WHO is going to use this(ie...clients?) I assume YOU will be engineering while someone ELSE is in the booth. And usually clients don't like to stop and open the door in order to get a breath of fresh air. No matter, you NEED it. But thats for you to decide. You asked. I answered.
Let me add this. There are a thousand ways people build their booths. Each is in direct relationship to the things I asked above. Compromise is the USUAL name of the game. However, if you are trying to record late at night, right over someones beroom, and your lease depends on not disturbing people, then the difference between success and failure is important. Thats why I suggest OPTIMUM isolation technique for the space and budget. Whether or not you need it, can build it, can afford it, or the existing structure can handle it, is totally in your ball park. If you only want a "quasi" iso booth, then I won't waste my time. ANYONE can suggest "moving blanket and PVC frame type assemblies. BUt if you are serious, and want to know HOW to do this, then we need to take a step at a time.
Ok, thats it for now. Once we know some things, we can better advise you on the plan. Later.
fitZ