You can use any of your favourite JavaScript/Ajax libraries with TurboGears.
Just put them in the static/javascript directory in your project’s package directory, like you would do with your own custom JavaScript code.
In your templates, you can include them like this:
<script src="${tg.url('/static/javascript/mylib.js')}" type="text/javascript" />
Some popular JavaScript libraries have been wrapped as TurboGears Widgets and can be found in the CogBin or downloaded through the Cheeseshop.
To use them, you just have to include the name of the widget object (including the name of the package that contains it) in the list of widgets in the tg.include_widgets setting in app.cfg, e.g.
tg.include_widgets = ['jquery.jquery']