There are two ways you can check the number of back links to your site or blog.One method is to type link:http://yoursite.com in Google search box .The number of results shown by this search query is actually the number of links pointing to your site.For example if I want to find out the number of links pointing to http://www.microsoft.com then I will write the following text in google search box :
This will give me the number of links pointing to the site http://www.microsoft.com . The other method is to install Google toolbar .
The other method to use yahoo for finding the links to your site.For this go to Yahoo home page and in the search box type :
To get a clear picture of how this works , watch this demo video .