1. Make sure your site is backed up. Then upload the Widget Context plugin.
2. Drop one experimental widget into your sidebar and use the settings to place it only on one particular page.
3. Start thinking about how you could use this!
If your site is NOT already backed up:
There are a number of good plugins for backing up your site — some free and some paid. This article contains a great, step-by-step tutorial on backing up a WordPress site using one of the free options.
I would ALSO call your hosting company to see what type of backups they have in place. If a problem occurs, it’s nice to know: 1. if they do nightly backups and 2. how easy it would be to restore your site if there were a problem. It’s just good to know.