I don't pretend to be an expert on Wesley, only a student of the man. Further, I don't accept uncritically everything the English evangelist taught because he was a High Church Sacramentalist Anglican priest and I am a Low Church Anabaptist, though I am pleased to be called a "Wesleyan."
Also, it's complicated because there would be a great divergence of opinion among people who align themselves with Wesley as their chief theological influence.
These days we Wesleyans may be defined (by others) by what we don't believe (or what they perceive we don't believe):
1. We don't believe in Total Depravity. (Well, some don't. I do but it may come down to semantics. While we believe that mankind is seriously warped by sin we don't believe that people are so sinful they—aided by prevenient grace—are still unable to choose or reject the Lord. John Wesley held to total depravity but it didn't lead him to Calvinism. )
2. We don't believe in Unconditional Election. (We don't believe that God chooses us to be saved without our participation.)
3. We don't believe in Limited Atonement. (We don't believe that Jesus died on the cross for the sins of only a preselected few.)
4. We don't believe in Irresistible Grace. (We don't believe that God has preselected some people to be saved and so they will be.)
5. We don't believe in Perseverance of the Saints. (We don't believe that all who are truly saved at one point automatically will remain Christians.)
In other words, we aren't Calvinists. That doesn't actually define us, though, does it? Here are some things we believe:
1. We believe that all of the world is under the power of Satan (1 John 5.19) but, aided by God's grace (John 6.44), we can choose to be saved. (Acts 2.40)
2. We believe that we have the ultimate choice as to whether we are saved from our sins or not; God wants us all to be saved.
(2 Peter 3.9)
3. We believe that Jesus Christ died on the cross as an atoning sacrifice for all of the sins of the world. (John 3.16; 1 John 2.2)
4. We believe that we, aided by God's grace, are free to choose to become Christians or free to choose to remain in a life of sin.
5. We believe that salvation is freely accepted and (sadly) freely can be rejected later by a Christian (i.e. "forfeit his salvation"). (John 15.4-6; Romans 11.17-23; Hebrews 6. 4-6; 10.26-31; 12.25)
This is a foundation of Wesleyan thought; we will look at Wesleyan distinctives in following posts. At this point you may ask yourself, "What do I believe?" If someone asked you for a summary of your beliefs, can you answer him cogently?
Remember Peter's admonition:
In your hearts be consecrated to Christ as Lord, and always be ready to make your defense to anyone who asks a reason for the hope you have. But you must do it in gentleness and reverence, and keep your conscience clear, so that those who bitterly abuse your excellent conduct as Christians may be ashamed of slandering you." (1Pe 3.15b-16)