How much it costs depends greatly on what you build and where you build it. It is possible to build a somewhat quiet, bare bones 8x8x8 room into a garage space for ~$500.00. More than likely, you'll be looking at closer to $2,500.00 min for any kind of reasonably quiet room with ventilation and a decent door. Costs go up dramatically from there. Generally speaking, the costs for sound proofing scale quadratically.
How much experience you need also depends on what you build. Something simple can be done with very little previous experience, but I would recommend getting help from someone with experience as this will prevent costly mistakes.