The International Phonetic Association created a system to represent the sounds of world languages. The Phonetic Alphabet is a useful tool for learning accents, too! Each symbol represents a single sound. Though it's hard to have a clear agreement on exactly what that is - the tool is used slightly differently by each person - there is a general agreement that serves well and is a transferable skill.
Some people make up their own alternative lettering system, but they're usually really crappy! These people must be stopped! Aaargh!
Yeah, it's not perfect, but at least it's something a bunch of experts agreed on. I haven't found a better way to talk about accents... Even the Lessac system of numbering many of the vowels, which I do use to some extent, has major limitations - especially when trying to describe sounds outside of typical General American. Though it's over 100 years old, the IPA is still the way to go.
Part 1: Accent vs Dialect vs Idiolect
Part 2: Phonetics
Part 3: Placement
Part 4: Intonation
Part 5: Helpful Hints
Part 6: Prioritizing Learning Accents