Holding priority, cast Dualcaster Mage by paying its mana cost.
When Dualcaster Mage enters, it triggers, targeting Faith's Reward.
Holding priority, activate Phyrexian Altar by sacrificing Dualcaster Mage.
Resolve the Dualcaster Mage trigger, copying Faith's Reward
Resolve the Faith's Reward copy, returning Dualcaster Mage from your graveyard to the battlefield.
Repeat from step 3.
This clever loop turns a simple recursion spell into a self-sustaining engine by letting Dualcaster Mage target the very Faith's Reward that will eventually bring it back. Every time you cast and sacrifice the Mage to Phyrexian Altar, you generate the mana needed to keep going while feeding its copy directly back into the stack. Because Faith's Reward continuously pulls the sacrificed Dualcaster Mage right back out of your graveyard, you can cycle the entire process indefinitely for infinite resources and triggers.