Since Ubuntu is a take-off from Debian, it naturally uses Debians packaging tools such as apt-get, to update and configure your system. You may also use the GUI tool, Synaptics Package Manager.
Here are some useful links and info:
Good info about packages (see CONTENTS for a lot more on using apt* tools): http://www.debian.org/doc/manuals/apt-howto/ch-search.en.html
Update all installed packages:
# apt-get update
Install a package:
# apt-get install some-pkg
See what's installed:
# dpkg -l | more
# apt-cache search someRE*
You can convert an RPM file to a DEB package (or to/from other common formats) by using Alien:
$ alien --to-deb somefile.rpm (will create somefile.deb)
Some other things to mention -- apt* tools use a local "database" to drive what packages are available and where to get them. Read the URL link above to understand how it works and how to keep it up-to-date so you always know what the latest packages are available.