I'm surprised this hasn't been asked here yet. Mormon services are a bit different, as you discovered. In the United States, there is generally a block of 3 meetings back-to-back including a sunday school, a mens' and women's time for instruction, and a sacrament meeting where the general congregation meets together. It sounds like the first meeting you attended was Priesthood meeting where the brothers study the words of scripture and modern Church leaders. Those classes usually have a single instructor each week. [Source]
Sacrament meeting is where any equivalence of a sermon would be heard. The primary difference between Mormon services and some others is the focal event of church meetings. The purpose behind holding a sacrament meeting is to take the sacrament and renew covenants made at baptism. The actual administration of the sacrament is the most sacred public meeting to Mormons. Hearing people speak and even interpersonal communion (socializing) is only secondary, though important. [Source]
Members of a ward, or local congregation, are invited to speak by the bishop or his counselors (the basic equivalent of a pastor) and will have some time to prepare a talk. Talks should draw from the scriptures, personal experience and testimony, and focus on the Savior. Note that comments made by church members over the pulpit at a sacrament meeting do not necessarily reflect the Church's official position on a topic or even Church doctrine.
The talks are meant to urge, inspire, and exhort all in attendance to come to Christ, to give them an opportunity to feel the power of the Spirit, and to strengthen their faith. Often, members will come with questions in their hearts and find answers in the words that day.
Counsel from leaders like a bishop sometimes occur over the pulpit, but usually this is private and individual, based on personal circumstances. The bishop and his counselors are supposed to meet with members regularly in interviews. There is no paid clergy, so all the service is volunteer.
Each member is also assigned two "home teachers" which visit their family once a month to share a gospel message, check on well-being, and be a friend and support especially when needed. [Source] In this way, instruction is given which might also help replace a typical sermon pattern. The bishop, his counselors, and others he calls on help organize these efforts. (It has also proven to be very quick and effective during disaster response, as home teachers immediately report in on who they teach, and bishops coordinate an effort if needed. [Source 1, Source 2)
So what you saw was apparently quite normal. Even once a month (the first Sunday), a fast and testimony meeting is held during sacrament meeting, where members forgo preparing talks and instead bear their testimonies about Christ and the gospel for the hour as they feel a desire to do so. Instruction is very member-to-member, you might say, but is guided by the direction of a bishop and other church leaders who also inspire and instruct. [Source]