Short answer: Wait. Do not restart Firefox or try to clear or reset anything, which will likely simply cause you to wait longer.
Long answer: When Zotero syncs with the server, requests go into a queue on the server. The time it takes for your request to be processed depends on the size of the request (i.e., how much data you're trying to upload or download) and the number of users currently syncing. Sync times may range from a few seconds to, for large/initial syncs at the busiest times, a couple hours. The majority of syncs are completed within seconds.
You can see the current status by hovering over the sync icon. For queued downloads, the tooltip will say “Getting updated data from sync server”, while queued uploads will say “Upload accepted — waiting for sync server”. These messages mean exactly what they say and do not indicate problems. If a sync has already gone through, the tooltip will also display the last sync time.
If “Sync automatically” is enabled in the Sync pane of the Zotero preferences—which is the default and recommended setting—and you're working in Zotero, Zotero may appear to sync constantly when in fact multiple successful consecutive syncs are going through. The “Last sync” time displayed in the tooltip will give you an indication of when this is the case. You can also always see what data has synced to the server by viewing your online library on zotero.org.
Files sync separately from data, and while files are syncing you will see a progress bar to the left of the sync icon. Hovering the mouse over the progress bar will show file sync progress.
If you've been waiting for a sync to complete for over two hours and a recent “Last sync” time isn't displayed in the sync icon tooltip, restart Firefox/Zotero completely and try again. (On Windows it may be necessary to manually kill firefox.exe processes in the Task Manager or to restart your computer.) If you then see no change for another couple hours, and no “Last sync” time displayed in the sync tooltip, start a new thread in the forums and an administrator will check your account.