Wordpress query string

In wordpress, I want to pull up all posts that are in the “web” category that is tagged “funny” and “video”?

Is there a query string construction that I can put in the browser that would do that? Or if not, how I can do with PHP code/query?

You can do it within WordPress. For example, create a Page Template for the page you want to display these posts, and in that template, use query_posts.