How can I install a package without installing some dependencies?

apt-get won't do this, but dpkg will.

apt-get download latexila latexila-data

That will download the binary .deb files but will not attempt to install them.

Now you can use dpkg to force install them.

dpkg --force-all -i <name of the .deb files you downloaded>

I will echo the warning in the dpkg man page here:

Warning: These options are mostly intended to be used by experts only. Using them without fully understanding their effects may break your whole system.

If your system is broken after attempting this, you can just try to remove latexila and latexila-data. Good luck.

Here are the instructions following the TUG page on TeX Live and Debian/Ubuntu:

1. Install vanilla TeX Live as root, system-wide.
2. Ensure that the only Debian TeX Live packages installed are tex-common, texinfo, and perhaps lmodern.
3. Add TeX Live's bin directory to ENV_PATH in /etc/login.defs.
4. Tell APT about your TeX Live installation by building a dummy package using equivs:

    $ aptitude install equivs # as root
    mkdir /tmp/tl-equivs && cd /tmp/tl-equivs
    equivs-control texlive-local
    # edit texlive-local (see below)
    $ equivs-build texlive-local
    $ sudo dpkg -i texlive-local_2011-1_all.deb

At the step "edit texlive-local", edit the Maintainer field and the list of the packages provided by your local TeX Live installation as appropriate. If you installed scheme-full except collection-texinfo as recommended, the file should look like this example

(Basically, one has to create a dummy package to fool apt-get)

For other ways, see also How to install “vanilla” TeXLive on Debian or Ubuntu? on TeX.SX.

after doing

aptitude install [packagename]

You have the question if you want to install all packages that are mentioned.. if there is a package you do not want to have installed like mysql-server because it is offloaded to another server insted of answering y/n answer with

:mysql-server