How does one invoke equity in a court?

Courts seem to have fused the courts of equity with the common law courts. Judges can apply both common law and equitable principles in deciding a matter. If there is a conflict between the two, do equitable principles take priority? How can we invoke equitable remedy?

I realize that this is not a trusted source for legal explanations, but here is a link for some background to my question: https://en.wikipedia.org/wiki/Maxims_of_equity