First, you need to frame the walls of your booth. It is helpful to build the walls in sections before you put them up, but you've got to make sure your measurements and cuts are accurate. You can fasten the frames to the existing floor and ceiling and to each other, but you should try to avoid using pre-existing walls as support, for better sound isolation. Be sure to frame your doorway, and keep in mind any air vents in the room as well. Also, don't forget to frame a spot for your window, and only frame a new ceiling for your booth if the existing ceiling is too high for the new walls to meet.
Now you need to stuff your walls with insulation. You can use any kind of insulation that is effective and available. Double up your insulation if possible.
Cut and hang the drywall over all walls or surfaces that will be visible, taking care to enclose the entire room without leaving any big gaps between pieces. It will save you a lot of future trouble if you route your audio cables during this step. Also, don't forget to cut out air vents in the room if you have central A/C and heating.
Seal all the cracks and crevices in the drywall with putty and trowel.
Install your window. There are several options and techniques that you can use, but here is the main idea: your window should be 2 panes of glass separated by at least a couple inches, and their faces should not be parallel. The space between the panes should be airtight, according to the experts at Recording Magazine.
Put down a pad like the kind used for hardwood flooring and then build your raised floor's frame. You can build a ramp from the doorway into the room or you can just leave a step up, whichever is practical. Either way, be sure to leave about an inch gap between the walls and floor's frame. You can fasten the frame to the existing floor, although this isn't necessary.
You can put insulation in the floor's frame if you wish, and then install your plywood subfloor. Be sure to leave at least 1/8 inch between the subfloor and the wall.
Paint the walls.
Put down hardwood flooring or carpet.
Install trim at the base of the walls. This is to cosmetically hide the gap you've left around the edges of the floor.
Now you can acoustically treat your sound proof room, and you're ready to start recording hits in your new booth!