In firefox, depending on what version of firefox you are using - i'm using 6.0.2,go to the website that you want to move. Then click on the firefox tab at the top left and then click on bookmarks. Click bookmark this page. In the bookmark window click on the down arrow next to the window where it says "bookmarks Menu". A larger window opens up and you can now click on " new folder"and name the folder while it is blue highlighted. After that you can just go to the link in the bookmarks, click and hold the click and drag it to the new folder.
Or you can go to the webpage, click open bookmarks and save to page to the new folder you make. Then you can open the bookmarks again, go to the old link to the website, right click and delete it from that folder.