The alternate CD is actually a mini-apt repository. You can download the point release alternate CD and then insert it into the machine while it is booted up, after burning it.
Then go to Software Center-> Software Sources and use the
Add Volume button to add the CD.
Image credit Jorge Castro
This will work, but the CD does not contain every package which might be installed on your system, as it only contains what is needed to get a working system(except for some drivers). You still need to update any other packages you want to update using your internet connection(s).
The default packages (and a few more) will be updated to the point release version. These non-default packages were on the CD as they are commonly installed, but not installed by default. These may include common drivers.
For Quantal and later:
Quantal no longer has an alternate CD. You can, however, use
AptOnCD as follows:
aptoncd on a Ubuntu machine (of the same version and architecture(32/64-bit)) with a fast internet connection and install it:
sudo apt-get install aptoncd
And use the update manager to update packages. You can also select packages with:
sudo apt-get install --download-only [packages]
which should get packages and dependencies into the
apt cache. You can then create an
aptoncd CD and burn it with the packages it gives you from the selection. You can select any package that has been downloaded since the last
sudo apt-get autoclean operation.