Do you want magento's default tag functionality? You could add the product attribute tag as multi select and enable it for layered navigation. Than you can do something like this:
Maybe this is not ideal because you want to use the tag name instead of tag value for this. There are a lot of layered navigation modules available who provide this kind of functionality to have this "nicer" url work. For example Amasty's layered navigation and ManaDev's layered navigation.
If you don't want this then you could think about writing a frontend module where you catch the tag name as url parameter and display the correct products accordingly. There's some code snippet in this post you can look at, this is using magentos default tags.
Get products by product tags
There are a lot of options depending on what you want exactly. Above are some ways to do it. If you require more information just let me know :)