Read articles about the history of Bollywood dance--the more familiar you are with the nuances of this dance genre, the better able you'll be to guide yourself though online dance lessons. Articles can be found on websites such as India Bazaar and Bitten by Bollywood.
Purchase appropriate clothing to practice Bollywood dancing in, such as workout capris, dance leggings, jazz pants or dance shorts, jazz shoes and a snug-fitting top.
Watch free videos of professional Bollywood dancers on websites such as YouTube, carefully studying their arm placement, facial expressions, posture and the freedom of their movement. The goal is not to emulate the dancers but to check your posture and placement against theirs as you learn, to ensure that you're perfecting your technique.
Take online dance lessons from a site such as MyBollywoodStudio and Bollywood Grooves. These sites feature professional, trained Bollywood dancers, and will help you polish your technique and learn new combinations. There are usually fees for these classes, which cost about $10 per month for unlimited access to dance lessons.