How can I install software or packages without Internet (offline)?

Check out Keryx; it's an offline repository manager.

How does it work? It lets you download updates and new programs (with dependencies) to your flash drive.

Its interface is similar to synaptic, but it works from a pendrive (it doesn't need installation). Unfortunately, the GUI needs wxwidgets, which don't come preinstalled on Ubuntu (they're cross-platform and installable from here and Ubuntu repository here). It can only install software in a Ubuntu system, but you can download the updates or new packages in any Linux, Windows or OS X.

Here you can find a tutorial.

Another detailed step-by-step tutorial is in this answer.

Launchpad also hosts downloadable files.

A screenshot:

A quick hack

A quick hack is to copy all the packages you downloaded for your install to his machine (detailed instructions here). The .deb files are stored in /var/cache/apt/archives, then in the other computer launch Synaptic and select File -> Add Package Downloaded and search the folder were you put the files and open it, accept all (or install from terminal using the command sudo dpkg -i DEB_PACKAGE_NAME).

NOTE:
This assumes that your package manager is not setup to delete the packages straight after install. It also assumes that you are running the same version of Ubuntu (10.10, 12.04, etc) and architecture version (32b or 64b).

A DVD repository

If you want the latest bug fixes and security patches available then have a look at this tutorial, which covers creating your own DVD repository.