I'm not an expert is SEO, i have this little site called facebooksearch.com, and i want it to be shown on the first page of Google for "facebook search" search results.
Any suggestions?
1. Create useful content
2. Build backlinks
3. ????
4. Profit
Seriously though, assuming your domain doesn't get taken from you, you should try to create some additional content on the page or G won't have anything to index. Concentrate on making the user experience high (low bounce rate, time on site, repeat visitors, ect.) and the rest will come.
I have a feeling you wont get far with that domain before Facebook takes action, since it contains their trademark in the domain.
from where i am (romania) i see it on the first page in google.com, you are ranking on 10th. do a little research on your competition searching for allintitle:facebook search and see what they are doing on their pages. then, try to get links from other sites with the facebook search keyphrase and variations as anchor text
LOL! Facebook making you an offer.