You need to be root to do this so if you have not gotten root yet follow my guide to root your phone here
There are two ways to do this, but because the kernel that was flashed when rooting doesn't allow the system partition to be mounted read/write from adb, this can only be done while typing on the phone's virtual keyboard. You can install a terminal emulator and busybox (if you haven't already) and do this for free. If not, buy and install "Root Explorer" from the Android Market
"Root Explorer" is a very handy app to have with a rooted phone so it is well worth the small cost of buying it.
First, download a modified camera file and copy it to your SD card:
The md5sum of the new Camera.apk file should be ab43b5d284bd21cb296a52f214ccab92
Root Explorer Method
Now using Root Explorer navigate to /system/media/audio/ui/ and click the button to make the directory read and writable. Then rename the files below and add a .bak extension to the following files:
Now, the files should look like this.
Now push the button to make the directory read only again. (if for whatever reason, you want to reactive the shutter sounds, change the extentions back to just .ogg.
Next we want to replace the Stock Camera.apk with a modified one.
First copy /system/app/Camera.apk to a safe location as a backup using Root Explorer then
copy over Camera.apk in /system/app, with the modified Camera.apk and reboot your phone.
Terminal Emulator Method
Alternately, you can so this from a terminal emulator using only free apps, but this is more complicated. (Busybox must be installed)
Also note that the phones internal storage is "/sdcard" and the actual sdcard is "/sdcard/external_sd" so depending on where you downloaded the Camera.apk to modify the commands below accordingly.
su# switch to root user
mount -o remount,rw -t yaffs2 /dev/block/mtdblock4 /system# mounts /system as writeable
cd /system/media/audio/ui/# begin renaming files
mv Cam_Stop.ogg Cam_Stop.ogg.bak
mv Cam_Start.ogg Cam_Start.ogg.bak# move and rename Camera app to SD card
mv camera_click_short.ogg camera_click_short.ogg.bak
mv Shutter_01.ogg Shutter_01.ogg.bak
mv VideoRecord.ogg VideoRecord.ogg.bak
mv /system/app/Camera.apk /sdcard/Camera.apk.old
cp /sdcard/Camera.apk /system/app# copies the new camera app from the SD card.
mount -o remount,ro -t yaffs2 /dev/block/mtdblock4 /system# mounts /system as read only