This site makes mention of a "Methodist lay pastor." What does this person do? How is this role different from the "pastor" in the Methodist Church? What type of religious training or education does this person have?
In the United Methodist Church, a lay pastor is a church member who has received training and can assist with preaching and care ministries, but does not have a formal seminary education.
The lay pastor can perform most of the duties of ordained ministers:
The certified lay minister shall preach the Word, provide a care ministry to the congregation, assist in program leadership, and be a witness in the community for the growth, missional and connectional thrust of The United Methodist Church as part of a ministry team with the supervision and support of a clergy person.
However, lay pastors cannot lead Holy Communion unless they receive special ordination to do so.
I expect in the context of your reference, the point is simply being made that the the mother of the author, Sandra Sue, has pastoral duties (perhaps leading a small group, Sunday school, etc), but is unpaid in this position, and has a professional career outside of the church.
The concept of a Lay pastor is not new, but is recently (in the last 10-20 years?) seeing a resurgence in popularity as a concept, at least in the U.S. The basic idea is that lay people (those without formal pastoral or religious training) should be heavily involved in ministry.
A brief explanation, from the forward of a book co-authored by my father, The Lay Ministry Revolution: How You Can Join:
During more than twenty years of pastoral ministry, I have often tried to fulfill the many expectations that go along with what I call a clergy-centered approach to ministry but have always ended up feeling frustrated and guilty. I never have enough time, never enough talent, never enough energy to fulfill all the expectations. And, while feeling overwhelmed, I have often observed laypeople who are gifted and willing to serve but remain stifled and unfulfilled in their expressions of discipleship. I believe that many of the frustrations of both overburdened pastoral staff and unfulfilled laity spring from the same source--the unbiblical division of God's people into categories of "ministers" and "non-ministers." And I feel strongly that the solution to both problems, and a key to the church's spiritual power, is to be found in the recovery of lay ministry.
Another related concept is that of Tentmaking:
Tentmaking, in general, refers to the activities of any Christian who, while dedicating him or herself to the ministry of the Gospel, receives little or no pay for Church work, but performs other ("tentmaking") jobs to provide support. Specifically, tentmaking can also refer to a method of international Christian evangelism in which missionaries support themselves by working full time in the marketplace with their skills and education, instead of receiving financial support from a Church. The term comes from the fact that the apostle Paul supported himself by making tents while living and preaching in Corinth (Acts 18:3).
Lay pastor is actually an official designation in the Methodist church. There is some formal training that goes along with it --but nothing that comes close to the training required of a fully ordained pastor.
I'm basing this answer on attending a Methodist church that has two fully ordained pastors and a lay pastor on staff.