It is quite a lengthy process to do by hand but the best way is to do the search in google.com (make sure you have disabled anything from google that collects data on your search behaviour first!)
Check each of the top 10 results to see if they have the exact phrase in url, title and description.
Check each result for backlinks using yahoo site explorer.
Have a look at each results pages page rank.
These factors will give a good idea about whether you can compete to get on the first page.
If you want software to do all this for you and save time try market samurai (they do a free trial) or traffic travis (free).