Simple church is not a monolith. Christians all around the globe gather simply and differently. Despite this, many commonalities do exist. At its core, those who meet simply look to the Holy Spirit and the Scriptures to guide church life. It is the Spirit who gives life. He opens our eyes to see in the Bible how God would have us live. What we read in the New Testament serves not simply as a description, but also as a prescription for how the church can and should function today.
Christ is the unquestioned Head of His church. We in the church are the body; all are of equal significance, and all are needed. Jesus leads and we follow. When we come together, the goal is to have a family gathering that glorifies Christ through the mutual edification of the body. We all have the joy and responsibility of edifying one another in Christ. During most gatherings we eat; this is the Lord's Supper. It is a beautiful time of all the members using their gifts to help the whole grow toward maturity in Christ.
Many times we meet in homes, but this is not required. Wherever mutual edification can occur is a great place to gather. A key component of the gatherings is the "one anothers." The New Testament is full of commands to carry out all sorts of one another functions within body life. The purpose of these (no surprise here) is mutual edification.
Simple churches can easily be generous churches. The reason for this is that everyone is encouraged to give as the Spirit leads. All the giving can go directly toward meeting real needs, either inside or outside the body. Simple churches basically have no overhead costs such as buildings and salaries. When churches come together decisions often have to be made. The goal is to seek consensus. This may take extended time and even get messy, but the result is unity. Unity is important because Christ expects and demands it.
Leadership happens through setting the example of service. Leaders don't lead through decision making, but by caring for the needs of others. Elders, who usually are leaders, come from within the church family. They are spiritually mature, respected men who lead by setting the example. This example is one left by Christ - the night before His crucifixion He washed His disciples' feet.
To sum up, simple churches strive to emulate the positive aspects of church life that we read about in the New Testament. When we seek to live this way it can be a glorious thing indeed.