I think I got it.
local string = "a:2:{s:8:\"td_video\";s:60:\"http:\/\/www.youtube.com\/watch?v=brSU-lAACiA&feature=autoshare\";s:13:\"td_last_video\";s:60:\"http:\/\/www.youtube.com\/watch?v=brSU-lAACiA&feature=autoshare\";}"
pattern = "v=(...........)"
local vidid = string.match(string, pattern)
There are 11 dots because Youtube video ID are only 11 characters. I'm not expert in making these patterns, so if there are other easier and shorter methods please share them with me.