Microsoft has just released a Firefox extension that provides auto-suggestions from Live Search right in your browser while you're typing your query. The officially supported add-on, written by the Live Search team in Microsoft, gives faster search results through this auto-suggestions feature.

Auto-suggestion means when you type a search term into the Live Search box, it shows relevant suggestions that match your search query and as you continue typing or when you change the query it refreshes the suggestion. You can click the suggestion that best matches you. You can install the add-on from here

According to them the extension is based on the Open Search standard and uses the JSON interface supported by Firefox to retrieve autosuggestions.[Via - blogs.msdn]