You do not download any packages. Basically you should NEVER download any
application as you would with Windows in Linux. It just isn't something that
you would do unless you know what you are doing and have a reason to do so.
You use the package manager. The package manager searches not your computer
for packages, but the repository which is online. Then if you select it to
install it will download and install it.

You can add outside repositories in Ubuntu and PPAs, but you still use the
package manager to fetch them and install. To download and install them
yourself you need advanced knowledge or you risk messing things up big time.
This sometimes involves compiling which isn't the biggest problem. You lose
the ability to upgrade them through the package manager and you risk
dependency errors when one set of packages is upgraded and another can't be.
This can lead to stability problems, freezes and crashes. You of course
bring it on yourself when you do this. Better to be safe and stick to the
package manager and established best practice.

Ubuntu ships with two package managers (Software Centre and Synaptic),
although that will change with 10.10. Synaptic will no longer be the default
package manager. You will have to install it separately. Gdebi will no
longer be shipped either. Software Centre will handle package management and
installing downloaded DEBs.

I prefer Synaptic or apt-get to Software Centre or KPackagekit. It is
standard across all Debian distributions and even some RPM such as PCLinuxOS
and it works well. Unlike other package managers you can select multiple
packages then leave it unattended while it downlaods and installs. Software
Centre requires you to participate throughout the process. Install, wait,
install, wait, etc.

You never realise how good Synaptic is until you use another package manager
such as Packagekit (Fedora), YAST (SuSE) or Yumex (Fedora). Software Centre
is set up for newbies, but it just does not cut it for experienced users,
IMO. But they all work off the same base which is repositories that are
maintained for co9nvenience and protection.