I have no idea how to start to download anything with this Torrent thingy..

while you wait for an answer please read the transmission's already answered questions:
https://answers.launchpad.net/ubuntu/+source/transmission

You need to open a torrent file with it, the contents will then be pulled down from the peers of the torrent, more peers = more speed.
http://www.legittorrents.info/

Here is a sample torrent site you can search and pull stuff down. Remember to NOT breach copyright. Canonica and Ubuntu do NOT condone piracy.

You need to download a ".torrent" file, for whatever it is you want to get.

For example, if you wanted to download an ubuntu iso, then you would go to your favourite search engine and type something like "ubuntu torrent"

Which could lead you to a page like so:
http://www.ubuntu.com/download/ubuntu/alternative-download

Then you download the ".torrent" file, and then drop it into transmission. The torrent file is only very small.

Once you do this, transmission will contact the "tracker", which is a server with a list of computers that are sharing this file. Once you have that, then you can ask for the file fragments from different users - theoretically obtaining a higher speed and reliability than possible from a dedicated server.

When the file is downloaded, the torrent file contains codes that allow it to check the file's integrity.

You need to find a .torrent file for whatever you want. Remember that bittorent is just a protocol, not a service. It is merely a method of reliably sharing files in a distributed manner.

There is a second way to get torrent files, using so-called "magnet links"

Here is more information about them:

http://code.google.com/p/itransmission/wiki/MagnetLinks

They are an alternative way to get chunks of data from the Bittorrent network, but without needing to download the small .torrent file.