I am implementing a tagging system on my website similar to one stackoverflow uses, my question is - what is the most effective way to store tags so that they may be searche
You can't really talk about slowness based on the data you provided in a question. And I don't think you should even worry too much about performance at this stage of developement. It's called premature optimization.
However, I'd suggest that you'd include Tag_ID column in the Tags table. It's usually a good practice that every table has an ID column.