TLDR: the best way is to find a local, structured class that will take you from zero to fluent.
Actually, there are a number of approaches you can take to learn the Qur'anic Arabic, depending on your location and means (time, energy, internet connectivity, and willingness to learn). These are:
- Take a local Arabic class. My personal favourite. These usually follow the cirriculum of the three books by shaykh Abdul-Raheem V., which focuses on grammar.
- Learn online. Find a reputable institute (like the Fajr Institute) and have online one-on-one learning with a shaykh who knows his stuff.
- Self-Study (The Three Books): The three books also have "Key" books which explain, in decent English, the lessons learned from each book; the perfect complementary resource for a self-studier.
- Self-Study (Online Websites): There are several resources online -- sites, videos, etc. for someone who wants to study Arabic. Look it up.
Personally, I've tried all of these, and nothing beats being forced to sit in a class every week and study -- it keeps you motivated, it keeps you going, and you can ask questions when you don't understand.