General conditions:
It is necessary that you set up a link to jquery. You can use one of the CDNs from Google or Microsoft or you create a central document library, where you store the jQuery file.
In the sourcefiles, where iam using jQuery, Javascript or CSS Stylesheets, i will use following placeholder for the jQuery/ Javasript-Path: *PathToJSLibrary* and *PathToCSSLibrary* for CSS-Stylesheets-Path.
Gallerific Slideshow for SharePoint
The first step to your Gallerific Picture Slideshow, is to download the Gallerific-Source-files from http://www.twospy.com/galleriffic/. Upload the jquery.galleriffic.js file into a central document library. Galleriffic is using the jquery.opacityrollover.js-plugin. So you should upload these file as well. (You will find all required files inside the galleriffic-2.0.zip from the Galleriffic-Website) Upload the basic.css and the galleriffic-2.css into a central style library.
After downloading and unpacking the Gallerific_Slideshow.zip from this repository you will find 2 Web Part files.
Open both files and change the *PathToJSLibrary* and *PathToCSSLibrary* with your path to the Galleriffic-jQuery-Plugin and Galleriffic-Stylesheet-files.
Create a new Page and click Add a new Web Part. Now you can Upload both Web Parts to your Sharepoint. Add both Web Parts to your page and you should see the Galleriffic Picture Slideshow.
Office 365 jQuery Sandbox Solution
find a german documentation here: http://office365blog.wordpress.com/2011/03/07/jquery-1-5-1-fur-office-365/