John Wesley died an Anglican priest and never intended to found a denomination. Methodism became one anyway, and the mechanism is worth following because it explains the tradition's shape.
The name began as mockery, aimed at the methodical devotional rule kept by a small group at Oxford in the 1720s. What turned it into a movement was Wesley's field preaching from 1739, an unrespectable practice that reached people the parish system was not reaching, and the class meeting, small groups of a dozen or so meeting weekly to give an account of their spiritual state to one another. That structure, not the preaching, is what made converts stick.
Theologically Wesley is Arminian, and the point is not incidental. He held that Christ died for all, that grace goes before any human turning, what he calls prevenient grace, and that it can be resisted. That set him permanently against George Whitefield, his Calvinist co-labourer, and the two parted over it while remaining on personal terms. His most distinctive teaching is Christian perfection or entire sanctification: that a believer may in this life come to love God and neighbour without reserve, as a second work of grace after justification. Wesley defended it constantly and was careful about what he did not mean by it, and it has been argued over inside Methodism ever since.
Separation came through ordination. Wesley wanted preachers and sacraments for the American societies after the revolution, no Anglican bishop would supply them, and in 1784 he ordained men himself. He insisted this was a presbyter acting in an emergency, not a bishop acting; the Church of England read it as a schism, and it was.