How to use grep and cut in script to obtain website URLs from an HTML file

I am trying to use grep and cut to extract URLs from an HTML file. The links look like:

<a href="http://ift.tt/1tkQYPP">

Other websites have .net, .gov, but I assume I could make the cut off point right before >. So I know I can use grep and cut somehow to cut off everything before http and after .com, but I have been stuck on it for a while.