You can't. Actual sound proofing requires total hermetic sealing and two layers of mass separated by an insulation-filled air space. doors and windows must be sealed, (just a decent door seal runs about $250) and then you need specially shaped ducting so you can still breath without ruining the isolation.
The closer you come to completely sealing the closet, the more isolation you can get, but without some serious DIY work and a few hundred in materials, it will NOT be very sound proof.
Some things that can help - record vocals when nobody else is home, or at 2 am if it's quiet outside (close the windows, or your neighbors will call the cops and you may get accused of brutalizing your singer) - leave the clothes in the closet, just push them aside, and put rolled up towels against the door at floor level, maybe hang a heavy curtain over the door - some people use furniture moving pads - harborfreight.com sells some pretty reasonable.
Also, unless you want no answers other than put-downs, keep in mind that TYPING IN ALL CAPS IS CONSIDERED YELLING, and rude.
sooo, turn off your Caps Lock and let us know if you need more advice... Steve