Atlast I got the answer for my question after spending a lot of time on this and getting support from EngineYard team.
First you need to create a local SSH Key Pair by following this article.
Next you need to add that SSH Key (something like id_rsa.pub or id_dsa.pub) at https://cloud.engineyard.com/keypairs
Then you need to execute this command in your local terminal
ssh deploy@ec2-xxx-xxx-xxx-xxx.compute-1.amazonaws.com
where
deploy
is the common and default username for your database andec2-xxx-xxx-xxx-xxx.compute-1.amazonaws.com
is your hostname