On Ubuntu you should try to stick to Ubuntu-specific .deb package files (as opposed to .rpm which are Fedora, Mandrake, SuSE etc. distribution packages -- the specific distribution is usually mentioned where you download the file). .deb files install by double-clicking on them, after which you should be prompted for your password. From command line,
sudo dpkg -i filename.deb
along with path to the file, if it's not in the same directory you're working in.
It's true that you can "convert" .rpm packages to .deb packages, but while that should work for many packages, it's not by all means "sure" way to do it. Distributions do differ slightly, so installing a "non-native" package (like a Fedora .rpm some way to Ubuntu, or even Debian-specific .deb on Ubuntu) could potentially cause trouble. Also try to avoid downloading and installing those packages one by one, if possible; if they have dependencies (other packages that need to be installed prior to the package itself so that it works), you need to obtain (search and download) them manually, and install in the right order or all at once. Using your package manager - in Ubuntu Applications-menu => Add/Remove tool, or Synaptic from the administration menu - you just find the package name you want to install, select it, click Apply and the program checks if other packages are needed, then automatically downloads and installs them for you. That's the easiest you can do today.
Winamp is nice on Windows (or rather was; the version they use nowadays - Winamp3(?) - is horrible compared to the previous version), but on Linux there are (better) alternatives. A Winamp-looking player is Audacious; it probably accepts Winamp skins too. XMMS was the old Winamp-"clone", Audacious is like XMMS further developed. Amarok is a "winamp + loads more" player, but it looks good on KDE desktop only if you ask me
on Gnome Audacious does better. Rhythmbox, which is in the Ubuntu reposities also, somewhat reminds iTunes, except that it works, and it's a whole lot faster than the Apple product. Just launch Synaptic from the administration menu, click Search and type in "multimedia" or "audio player", and you should be presented with loads of options..check their websites, and see what looks good.
Note that on Linux there are both such players that contain both the graphical interface and the "engine" that does the job of decoding the files, and players that are more like "front-ends"; they are the user interface, but in addition to them you need a (transparent for the user) "backend" or "engine" that then deals with the real playing/decoding part, and is controlled by the graphical app you see on your desktop. The main two "backends" or "engines" are Xine and GStreamer. Both will play most of the formats you meet; I think Ubuntu uses GStreamer by default, and it's ok. Don't go switching it unless you are ok with spending some time replacing apps (like totem-gstreamer with totem-xine, to make it work with the new engine) and obtaining new codecs/libraries to support various formats. MPlayer is then an example of a player that comes with (some) codecs/libraries "builtin", and it doesn't need a separate front-end player app (MPlayer as such is launched from command line, but it comes with graphical user interface - skins - that you launch as 'gmplayer' ('graphical' mplayer?)).
Well, this is a subject you could read, write and study for ages. Ubuntu website (Wiki) has a lot of information for you if you need. Basically if you have a file format that your system says it doesn't support, try to open the file with Totem and it ought to ask you if you'd like to search for a codec. Accept the offer, and with some luck you'll be playing the file with your favourite apps in a moment (it's a Gnome + distribution package management ability to try and search the reposities for the right codec package for the engine, not built into all Linux operating systems and desktops).