My son was assessed at 13 months. I called up EI in my state and they set an appointment first to come speak to me, and then to evaluate my son. The evaluation was done by an SLP and a nurse. I don't recall how long it took - maybe an hour. My son enjoyed it - they just played with him more than anything to see where he was developmentally. They also asked me questions. At the end they explained what they observed and showed me how he scored. We qualified for services because his speech/language scores were so low. I accepted services, and another appointment was set up for paperwork to line the services up. That was it.
It may be slightly different in your state, but I have offered this description to quite a few parents and never had anyone come back and tell me that they had a grossly different experience. I was very happy with how everything went, although the nurse irritated me a little (her mannerisms mostly).