Where to start
If you just want a simple way edit collections on the Kindle using a GUI - then you can install the Calibre plugin and select "Edit Collections" as Ajax pointed out. It reads whatever collections/books you have on the Kindle, allows you to create/modify/delete collections in a simple GUI, and save them back to the Kindle. It even makes a backup copy of the original collections file. The books don't need to be in Calibre. Its really a separate program but uses Calibre to make it easier to write/distribute/install.
But if you want to use Calibre, then as CRussel and Leep said you can create a new custom column in Calibre to hold the collection names per book that you want to write out to the Kindle. You can even import your existing collections from the Kindle to get started quickly. Using this approach, the plugin can only create collections containing books that are in calibre. But you can still manually create other collections on the Kindle yourself (or using "Edit Collections"). There is an option on by default that means any collection names that don't match what the plugin will create will be left alone. And to be extra safe there is a field you can use to never overwrite specific collection names.
@chamekke - yes the plugin can certainly automatically create collection names from tags, authors, and many other fields (such as a custom field above). Again, this only works for the books in Calibre. But you can create collections manually on your Kindle that contain any books and the plugin can be told to leave them alone. There's even a Preview report to show you what will happen without doing anything.
@HarryT - This means you can use the plugin to create collections using your custom column name or Authors or Series, etc. for books that are in Calibre AND also manually manage other collections on the Kindle for any books not in calibre. It might be that just using "Edit Collections" is all that you need, especially if you've already got everything setup the way you want and don't want to be too worried about keeping calibre/non-calibre books in separate collections.
@Lozh - hmm, maybe that makes it sound not too easy. I think it depends on what you want to do. It can be very easy (just GUI edit directly), or just a bit more complicated and limited to books in calibre depending on what you want to accomplish. There is a lot of flexibility in the plugin due to all the feature requests from users (its 2 programs in 1) - it can even adjust your horizontal margin or allow left/full justification which doesn't have much to do with collections (or is that 3)
Oh, and installing the plugin is a lot easier now. Calibre now has the ability to Get and install new plugins automatically. Use Preferences -> Plugins -> Get new plugins (or use the down arrow on Preferences to select Get new plugins...)