Determine the function of your booth to aid you in design. Keep in mind that true soundproofing requires isolation and mass: things like false floors, thick walls and ventilation systems. Likewise, acoustically superior rooms feature non-parallel walls, a variety of reflective surfaces and a volume in cubic feet that is not practical for the average home.
Design an enclosure if maximum reduction of sound level is your priority. Frame the walls using two-by-six-inch lumber for floor and ceiling plates, connected by two-by-four-inch studs on 16-inch centers; but run an inside and outside row of studs, alternating sides every eight inches. Weave mineral insulation between the studs, then staple the open weave fabric to finish the interior walls. Use wallboard for the exterior, and fit the booth with a solid wood door. Consider four feet by four feet to be the minimum internal dimension.
Create a three-panel hinged "gobo" (go-between) wall for moderate sound reduction and acoustic control over unwanted room sound. This may be the more versatile option if you are a home recordist looking to improve isolation and vocal sounds. Construct three panels, each measuring three feet by seven feet, from two-by-four lumber. Stuff the panels with mineral insulation. Cover one side with open weave fabric and cover the other with wallboard. Hinge the panels together so that the outer panels swing in to create a self-standing baffle.