Hi, I'm not a regular here, and I'm not very articulate either, but here's my attempt at answering your question:
Pretty much all Anabaptists (including the Amish) believe the following:
1) Believer's baptism. You decide to follow Jesus and be baptized as an adult. Infants cannot decide this and therefore shouldn't be baptized.
2) Importance of church community life. You cannot be a Christian all by yourself. The body of Christ has many members, and we need to minister to one another, serve one another, encourage and support one another, admonish one another, teach one another, share with one another, and strive to live faithfully together. There is also a strong tradition of "the priesthood of all believers," which simply means that each Christian is equal in the eyes of God and that nobody like the Pope or Cardinals or such have any higher authority. This also means that everyone is free to read and interpret the Bible, however, it is most important to do this in community where we can benefit from the Spirit's speaking in each one of us, as opposed to only the Spirit's speaking in ourselves alone.
3) Faithful living. Your lifestyle matters. Obviously we're all sinners, and we can be forgiven by God's grace, but that doesn't mean you can just jolly well go on living however you please. We need to strive to be faithful to Christ in all that we do. Your lifestyle matters.
4) Nonviolence and peace. Christ called us to love our enemies, and we take that literally. Killing or hurting your enemies means you're not loving them. We need to strive to promote peace in the world in a nonviolent manner (and that can take a lot of work!), not just sit back in passivity.
5) Importance of Scripture. If Anabaptists had to choose only three chapters of the Bible to live by, it would probably be Matthew 5-7, the Sermon on the Mount. If we were allowed to choose a larger section, it would be the four gospels, and maybe the book of Acts too. The rest of the Bible must be interpreted in light of the gospel of Jesus Christ. (We also like the entire Bible, don't worry!)
The distinctive lifestyle of the Amish comes from Jesus' teachings to live simply and faithfully. All Anabaptists believe that simple living is important, but the way that different groups live this out is quite varied.
I hope this helps. It's the best I could do off the top of my head.
