Who was the mormon leader who brought his followers to the shores of the Great Salt Lake in 1847?

You're thinking of Brigham Young... but in reality, Brigham Young was not named the President of the Church of Jesus Christ of Latter-day Saints (commonly called the "Mormon" church) until after they arrived in Utah. Joseph Smith had told Church members that they would have to move to the Rocky Mountains, and after he was murdered it was decided that was what they should do. Brigham Young, one of the Twelve Apostles at the time, had received a vision of the Salt Lake Valley, and so he was put in the first group. When they arrived in the Salt Lake Valley, he declared that it was the right place and sent for the other groups of pioneers. Mormon Pioneer groups traveled the plains to Utah for the next 20 years, after which they were able to take the train. Also, they certainly did not go to the shores of the Great Salt Lake. Salt Lake City is about 25 miles from the nearest 'shore', which is surrounded by a large marshland and smells so bad that people still don't live any closer to it.