Be aware of the issues. Websites such as Asian Elephants Today (asianelephantstoday.com) have news about Asian elephants and the plight they are facing. Once you know about the problems affecting Asian elephants, you can work to address them.
Donate money. Organizations such as EleAid (eleaid.com) have several initiatives to protect Asian elephants in the wild. You can support individual initiatives or donate money to the foundation for allocation as it sees fit. In some cases you can even sponsor an individual elephant at a sanctuary or preserve.
Volunteer with an organization that's working to protect Asian elephants. Look for opportunities posted on company websites. If you don't see any listed, send an e-mail. Ask how you can get involved and what you can do to help conservation efforts to save the Asian elephant.
Know what you are buying. One of the biggest threats to elephants is loss of habitat due to deforestation and over-farming. Check where your products are bought, and avoid those made in areas where this threat occurs unless you are certain production does not affect the elephants' habitat.
Sign a petition. Asian Elephants Today has a list of petitions across the Internet that address issues facing Asian elephants. Pick a cause with which you sympathize and add your name to that cause. Consider also writing a personal letter and addressing it to the recipient of the petition.