How to write to a Mac OSX read-only filesystem?

Almost all read-only DMGs are actually compressed (UDZ0 -- see the hdiutil(1) man page), so their file format doesn't support simply "flipping a bit" to make them writable.

You could use Disk Utility or

hdiutil imageinfo filename.dmg  

...to see what format your disk image is in. Then you could use Disk Utility or something like

hdiutil convert filename.dmg -format UDSP -o filename.sparseimage  

...to convert it to a read-write format. Note that the conversion does not happen in-place, so you'll have to tell it to put the output file on a filesystem that has enough room for an uncompressed copy of all the data from your .dmg.

The .dmg extension does not guarantee that the image is actually compressed, but that's by far the most likely possibility.

There are several other possibilities available to you with hdiutil. For instance, if your .dmg is actually uncompressed read-only (UDRO), it might be possible to force it to mount read-write. Also, if you want to leave your .dmg compressed but still want to mount it in a writable fashion, you can mount it with a "shadow file"; all writes actually get written to the shadow file.

Update: Other Answers on this Question seem to think .dmg always means UDZ0 which just isn't true. From the hdiutil(1) man page, here are the list of internal formats a .dmg can have (note that a couple of these can have different default filename extensions like .sparseimage, but I'm pretty sure that's not a hard-and-fast rule either).

UDRW - UDIF read/write image  
UDRO - UDIF read-only image  
UDCO - UDIF ADC-compressed image  
UDZO - UDIF zlib-compressed image  
UDBZ - UDIF bzip2-compressed image (OS X 10.4+ only)  
UFBI - UDIF entire image with MD5 checksum  
UDRo - UDIF read-only (obsolete format)  
UDCo - UDIF compressed (obsolete format)  
UDTO - DVD/CD-R master for export  
UDxx - UDIF stub image  
UDSP - SPARSE (grows with content)  
UDSB - SPARSEBUNDLE (grows with content; bundle-backed)  
RdWr - NDIF read/write image (deprecated)  
Rdxx - NDIF read-only image (Disk Copy 6.3.3 format)  
ROCo - NDIF compressed image (deprecated)  
Rken - NDIF compressed (obsolete format)  
DC42 - Disk Copy 4.2 image  

Here is method I just used for a project and was by far the best way to do this. Found it here:

http://myjeeva.com/best-possible-way-edit-read-only-dmg.html

Attach read-only dmg file using hdiutil

hdiutil attach -owners on /path/to/your.dmg -shadow

Modify your DM. Use the command line to add, edit or delete contents - doing it in the GUI can have weird side effects or permission issues. Additionally, you may need to sudo the commands

Detach mounted drive by below command or Eject it from Finder

# fill disk number at <number>
hdiutil detach /dev/disk<number>

Converting/Writing a shadowed dmg into read-only DMG

hdiutil convert -format UDZO -o /path/to/new.dmg /path/to/your.dmg -shadow

if there's enough "space" on the Rd-onry DMG, you can convert to a R/W DMG using Disk Utility, and convert it back to a compressed DMG if you want. Otherwise, you can "expand" the DMG using hdiutil