It's actually not that tough to do...
Take the new halyard's bitter end and attach it to the old halyard's bitter end. You can do this with a LOT of electrical tape. I've seen others that take a metal paperclip, bend it into an "s" shape & hook the two lines together before taping them up. This will, in effect, give you one long line. Once they're attached, just pull the new line up the mast, through the masthead & back down. Remove the tape & paperclip. Your new halyard will now be installed. For the proper length of line to use, check out this link: http://www.tcsn.net/bosun/c30/riggingdimensions.htm