By default, jquery will not be recognized in typescript files you create. This means that any jquery code you use will show up as erroneous and you can't make use of the auto-complete functionality. However, this is easy enough to remedy as shown below.
Copy the typescript declaration file into your project from here. Unfortunately the download links do not appear to work so you have to manually copy/paste.
Place the content into a file called
jquery.d.ts in your project.
Add a relative path link to that file at the very top of your typescript files that require jquery. For example:
/// <reference path="../../jquery.d.ts" />