To integrate jQuery into Application Express you must first download the library from jquery.com. For performance reasons i would recommend downloading the production version.
Once you have downloaded the file you have to upload the file into APEX. Do this using create image within shared components
Now that the jQuery library is stored within APEX you can access it using the following code
(you can upload the file to a specific application. if you do so then you must use #APP_IMAGES# instead of #WORKSPACE_IMAGES#)
This code can either placed inside the specific page where it is needed, or accessible to every page by placing it on page zero. If you wish to put it inside a page the sensible place to put it would be in the html header
Or, personally I prefer to place it inside the page template. This can be found within shared components.
For specific uses of jQuery please refer to docs.jquery.com/Tutorials