There are two ways to do this and I will detail them below. What they do with the exported files is completely up to them after the export. They can use them wherever they choose including Google sites as you mentioned.
1. Students can export the entire portfolio into a zipped file. They log into their accounts, and click the Export Portfolio link toward the bottom of the menu and then choose the type of export. This will take some time if their portfolio is large, so please advise them to be prepared to have their browser busy for a time.
2. Students can export all the files they have uploaded to Foliotek (vs. the entire portfolio) by going to the Files tab and clicking ‘Export All To Zip’. This will just be a listing of files they have uploaded to be viewed independent of the portfolio.
You can go through these two processes yourself to get a better understanding by using the test student account. Please do not hesitate to call me if needed.