How do I find out how many times a particular word or phrase searched
for on the internet in last month?

I do not think there is any way to determine how many times a
particular word or phrase has been searched for on the entire
Internet. There are thousands of search engines, and there's no
central body that monitors all of them.

Overture's "Keyword Selector Tool" may be of some use:

http://inventory.overture.com/d/searchinventory/suggestion/

http://searchenginewatch.com/facts/article.php/2156041

Google's zeitgeist is best