If you invoke apt-get from a pure console, assuming tty3, (not xterm), you may, as root, call:
Code:
setterm -dump 3
which grabs the screen of tty3, and writes it to a file screen.dump or similar.
Rename the file immediately, because the next command will silently override it.

If you know in advance, that you like to review the output, you tee the output.
tee stands for the big letter T which is a graphical representation for a three-ended pipeline.
Code:
command -> _______ _______> screen
                  T
                  |
                  |
                  V
              logfile
(surely the best graphic which was ever seen).

The command is:
Code:
apt-get install foobar | tee apt.logfile
tee will silently override existing files.
If errormessages need to be logged, which usually goes to a separate stream (errorstream, 2) , while normal output goes to outputstream (1), but both normally occur mixed on the screen, tee normally only grabs the outputstream.
To get the errorstream too, we redirect it to the outputstream:
Code:
apt-get install foobar 2>&1 | tee apt.logfile