Find a space. This might be a space in your home, such as a basement or garage, or a business location that you are going to lease if you want to build a commercial studio. In either case, you want a space that is already relatively noise free, as it means less work to reduce outside noise later.
Plan out your studio based on the space that you found. You need at least two rooms. One will be for recording, and the other a control room. The recording room should be the bigger of the two, as smaller rooms sound poor in recording situations. You may also build a third room to function as a vocal booth.
Hire a professional contractor to frame in your walls, as this is the best way to avoid mistakes being made. The framing can be regular internal framing, as the special modifications for a studio will be made later. You also need to make sure that you have plenty of electrical outlets in both the control room and the booth. Have an electrician come in and add more if there are not enough.
Insulate and cover your walls with sound-deadening material. There is special insulation called Rockwool that is used in many studios for dampening sound, but other sound-insulating materials will also work. Then apply the drywall, using a double layer of drywall if you need increased sound insulation from the outside world.
Build a cable pass through into the wall. You need cable boxes that will run all of your essential inputs from the recording room to the control room. You can buy pass through boxes from studio supply businesses. Have several XLR inputs and several 3/4 inch inputs running to your booth.
Lay carpet on the floor of the recording booth, and cover the walls with studio insulation based on the manufacturer's instructions for the brand that you purchase. To get the best possible sound quality, have a professional studio designer come in and install your insulation. He will know how to test the space and to install the right type of foam, as well as additional features such as bass traps to get the best possible quality out of the room.
Add furniture such as a desk and chairs to your control room and chairs and instruments to your recording room. Install your computers, consoles and rack equipment in your control room.