Master basic tango technique first. You need to have a solid foundation, including traditional footwork, turns and entries. Once you are comfortable with the Stroll, Ochos and Giro, you can focus on showier, more challenging moves.
Diagram the moves that you want to perfect. Identify weak areas for you or your partner.
Take a lesson or watch an instructional video. Check out dance schools and adult education offerings in your area. Look at dance diagrams, videos and other tango resources. Many tango instructors, dance scholars and enthusiasts provide tips and techniques online. For example, the Society of Dance History Scholars (SDHS) maintains a website with links to excellent tango websites.
Learn both the men's and women's parts. This helps you to internalize the rhythms and complexities of the tango. Experiencing and understanding the tango from both roles increases your dexterity and helps you and your partner to help each other improve.
Watch others dance. Sitting out a few dances is as helpful in perfecting your technique as the hours spent on the dance floor. Tune in to ballroom dance competitions and search online for videos of expert and aspiring tango pairs. Fifty years ago, many people began their tango lessons with simple observation.
Enter competitions. This will challenge you to continuously improve your tango technique, since you will be evaluated on your performance. There are often several levels in a tango competition, but all require you to perform classic tango movements. For example, your choreography may be judged on whether you have your knees open or closed during a saccade.
Practice makes perfect as you perfect your tango technique.