What were the major steps that Octavian took to gain the supportif the army and the people after defeating Antony in 31 bc?

You have to back up a little here. Octavian already had the support of the army and the Roman people before he had the senate declare war. A poll was taken throughout Italy and the people swore to support Octavian. He already had a huge army and the Roman troops that Antony had also went over to Octavian. So Octavian actually had little to do after defeating Antony at Actium except to pay the troops.