Like I mentioned in the title, your iPhone/iPod will need to be jailbroken for this to work. The app store and Cydia have both blocked this app from their repo and although it may be use to pirate content it also has it's legitimate uses.
First we'll open up Cydia, then click on the Manage tab on the bottom.
Click on Sources, this is where we'll add the iTransmission repo then click edit.
Click Add and type in the URL listed below. If the URL doesn't work, try googling iTransmission repo for another repository.
A warning will popup telling you that this repository has been reported by the community.... Go ahead and click Add Anyway.
You'll now see the insanelyi Repository in the list of sources.
Browse the insanelyi Repository and install the iTransmission package. Once the installation is complete you will have successfully installed iTransmission onto your iPhone/iPod and are ready to start downloading torrents.
Open up Safari and browse to your favorite torrent downloading site. For this example I will be using http://www.piratebay.se
Each torrent will have a magnet link and a torrent link. iTransmission accepts both of these. To add a torrent in iTransmission you will need to hold down either the magent or torrent link and then copy that link. We will be pasting into the iTransmission app. In the image below I have circled a magnet link and a torrent link.
Now open up the iTransmission app. Click on the + icon on the bottom. This is where we will paste our torrent url or magnet link. You may also choose a torrent from your filesystem but I will not be going into that in this tutorial.
Click OK and should see your torrent's download progress.
As you can see, the download speeds are decent all depending on your internet source. iTransmission does allow you to download with 3G as well.
Now if you want to see some of the dtails of your torrent such as the files contained and the download location you can click on the torrent. As you can see the download location is /var/mobile/Documents/Downloads
Once the filed has completed, I would recommend that you remove the torrent from iTransmission. Make sure that you choose Yes but keep data. Otherwise, your data from the torrent you just downloaded will be gone.
Using a file browser such as iFile, you may browse to where you torrent files were downloaded to and do what you would with them.