- Offload as much as possible into the webspace provided by your ISP. There probably won't be much space (enough for a few big images or MP3s), but the bandwidth should be free.
- Sign up for some temporary hosting with NearlyFreeSpeech.net. At $1 per 1GB transferred, the bandwidth fees are probably less than the excess bandwidth charges from your normal host.
- Provide torrents for bigger files (>5MB):
Instead of using one of the multitude of unreliable and slightly dodgy BitTorrent trackers, the best bet is to ask a friendly and reliable tracker server, perhaps f.scarywater.net or waxy.org/bt, if they'd mind hosting your torrent for a while.
Creating a torrent file is quite straightforward, using Azureus. Basically, you choose 'Create Torrent' from the File menu; select the 'file' or 'directory' option, depending on whether or not you're distributing multiple files in one package; enter the announce URL for your chosen tracker (ask the tracker administrator for this if it's not given on the tracker page); select the files to share, then press Finish.
This will create a torrent file in the same directory as your shared files. Upload this to the tracker, wait for it appear on the tracker page, download the torrent file as normal, open it with Azureus and choose to save over the top of your existing files. Azureus will then recognise that the files are complete and should start seeding (but if the status stays on Queued, right-click and choose Force Start to force seeding to begin).