There are many good examples of how to use Jquery with ColdFusion including how to make a simple Ajax call to a ColdFusion Component if you Google it, but this comprehensive example shows you step by step how to connect to a ColdFusion Component using Jquery/Ajax and get back some results to show on the page instantly.
My example is a basic form submission which sends an email to the email address you entered in the form.
When you click "submit" it triggers the Ajax function. Instead of submitting the form or reloading the page, the ColdFusion Component sends an email and returns the results so you can display an alert on the page for the customer.
The page looks like this, with a simple form.
Click here for a live demo
Download the sample files. (zip)