Do you mean you want the user to be able to browse to YOUR computer? Or do you want the user to be able to browse to HIS computer?
I think you might mean the latter, which is easier. You just need to use the <input type = "file"> tag, which will put a text box and then a "Browse..." button next to it.
If you do indeed mean the former, you're going to need to set up an ftp server on your computer and then just link to the location.