Since JavaScript is usually interpreted by a browser, the browser is one of the best debugging environments available. In particular, a JavaScript “console” is terrific for interactively interrogating the DOM, testing jQuery selectors against actual markup, and refining JavaScript code in real-time.
My preferred browser-based tool is the Firebug addon to Firefox. I cannot praise this Firebug highly enough. It has revolutionized how I approach client-side development, both of JavaScript and of CSS. If you prefer Internet Explorer, IE8's updated developer tools are also very capable in this department.
Whatever your browser of choice, I urge you to give these utilities a try when debugging client-side functionality. Once you become proficient with one of these tools, you'll be amazed that you ever developed client-side code without it. Get the VSDOC.
Even though browser-based tools are great for debugging, an ASP.NET developer's primary editor is still going to be Visual Studio. When writing jQuery code in Visual Studio, having proper Intellisense can make a tremendous difference in productivity. The discoverability that Intellisense provides is especially beneficial when you're unfamiliar with jQuery's API.
As part of the official support for jQuery, Microsoft provides a documentation file to provide jQuery Intellisense inside Visual Studio 2008. This is provided through what's called a vsdoc file, and is available on the jQuery download page (via the “Documentation: Visual Studio” links).
Jeff King has assembled an excellent FAQ to help you get Visual Studio 2008's JavaScript Intellisense working: http://blogs.msdn.com/webdevtools/archive/2008/11/18/jscript-intellisense-faq.aspx
