I'm not conservative, so I don't know exactly, but I'd assume they'd test you on what you studied and learned about Judaism, along with questioning your commitment to becoming Jewish.
From the A Conservative/Masorti Rabbinic Bet Din of Metropolitan Chicago website - http://www.jewishconversionchicago.com/requirements
"The Religious Court, or Bet Din, consists of three people, usually Rabbi’s or Cantor’s. The Bet Din officially oversees the formal conversion. Individual rabbis will provide guidance about how the Bet Din works. Because it takes place after learning, one part of the appearance will be to determine the Jewish knowledge of the conversion candidate. There might, for example be a question about the meaning of the Jewish Sabbath or about the Jewish belief in one God. These questions are not meant to trap candidates. Obviously, candidates are nervous during such questioning, but in almost all cases the questions are simply meant to assess the sincerity of the candidate and to make sure the conversion was entered into freely. "